“Oh, I’m sorry, she couldn’t make it.” (Of course, the OP will be RSVP-ing, letting them know that he’s attending, so they’ll know ahead of time she won’t be there)
Weddings are expensive – ask a third party. But do NOT simply assume she’s invited, or put the bride on the spot by asking her.
It only has your name, not her’s, nor does it say, “and guest”. Remember what they say about assuming? She’s not invited.
If these were CLOSE friends, I’d politely ask if it was an oversight.
Given that you pointedly say you are not close with them, I think it’s safe to think that they invited who they intended to invite. Every wedding has a limit on the number of guests, and while I think it’s a bit rude to invite someone and not their long-term partner (if you two are that far down on the list, they can invite neither of you in favor of another uncle, or something), it would be much more rude to assume your GF was invited without an explicit invitation having been extended to her.
Your GF was not invited. It would be rude for her to attend.
I don’t see the big deal about attending without a “date.” What, you can’t be apart for an evening? Really?
(1) It’s OK to talk to, even dance with, someone you’re not in a relationship with. Plenty of men don’t like to dance and are perfectly OK with their SO dancing with someone else.
(2) At the Chinese wedding I went to years ago, there wasn’t any dancing. About a million courses of food, but no dancing.
If its a traditional Chinese occasion - every one I’ve been to the tables are sat at 10 to a table, with communal style dishes.
One extra person isn’t usually a problem (just pull an extra chair to the table and squeeze a bit) BUT - if two or three at the table bring an extra, then it becomes an issue
Just chiming in - It would never occur to me that significant others were NOT invited. Bring her along and mark ‘2’ for attending.
As someone putting together a wedding invitation list right now - if your name isn’t on the invitation, you are not invited. There aren’t many people on our list without partners, but we’ve made sure we know everyone’s status. No SOs were left off on purpose.
But I could see others making a mistake or assuming wrong, or possibly inviting spouses but not significant others. The general rule is if you have any doubts, ask before assuming.
If her name is not in the invitation she is not invited. That they have met her and know you are in a long term relationship and still excluded her is IMO rude.
If I couldn’t invite both halves of a couple then I would invite neither.
It could be an oversight on their part but since they have met her in other social situations then I think it is a snub. Perhaps they have a single woman in mind they would like to introduce to you?
I think what causes confusion though is, some of us will follow the rules of etiquette to the letter and others won’t. Life would be a lot easier if everybody knew the rules and played by them.
It’s why some of us get upset over things like including gift registries with the invitations and asking guests to contribute to the honeymoon fund. It’s not just that it’s crass but it also starts bending the rules which causes this kind of confusion.
You don’t know who is following the rules and who is more relaxed about them.
I have to say that I am very surprised at the people saying so matter of factly that they would just bring her or write “2” in the box for number attending. If her name isn’t on the invitation or “and guest” she isn’t invited. Sure, it could be an oversight but do you really want to put the host/hostess on the spot by asking? Weddings can be expensive and a plus one could add a couple of hundred dollars to the cost of the affair. I wouldn’t presume or even ask but go alone or send a gift.
Please don’t ever just do that. No.
If my committed long-term partner is left off the invitation? Yes, I do.
My two cents:
How hard is it to just ask? Jiminy crickets. All this debate is stupid because it’s a mixed-culture wedding. Don’t assume she’s invited. Don’t assume she’s not invited. Just ask.
I agree that it’s okay to ask. I don’t think it’s okay to put someone on the spot by asking via a phone call in real time. Rather than ask the person in a way that could potentially catch them off-guard, think about other options. Ask through a mutual friend, or even in an email, so that the bride and groom have a chance to figure out how to make a gracious reply. Maybe that’s “my goodness, we apologize for the oversight, we absolutely intended to include her” but even in the best case scenario, I know I would appreciate the opportunity to have some time to figure out what had happened and what my response was going to be.
RSVP for one. That gives them a chance to ask why your SO can’t make it if it really was indeed an oversight or miscommunication. Two weeks before the wedding if you haven’t heard from them, send your regrets.
Obviously, it’s best to ask. Anecdotally, I have found that invitations for Chinese weddings often imply that you can bring guests (or family) even if it doesn’t explicitly say so on the invitation itself. I literally attended two weddings this summer that were like that - in the first case it was clarified through discussions with the bride directly and in the second case through the groom’s mother - in the second case it was the groom’s mother who called to ask if I was attending, even though I wasn’t on the invite (only one went to my parents) 
I can’t believe the people who would bring someone extra who wasn’t invited. There are many ways that your SO could have been invited. Both your names could have been on the invitation, she could have received her own invitation or yours could have said “and guest”. I find it hard to believe that they would have set up an RSVP so that every person invited could respond for up to 5 additional people.
I don’t think there is any harm in asking politely. Maybe you could call to RSVP no but explaining that while you’d love to come you have promised to spend your free time with your SO but if you were unentagled you would have certainly been there. That gives them the opportunity to graciously state that of course they meant to invite both of you or just as graciously accept your answer.
Asians don’t think like that. It’s cultural. In India, an invitation implies your entire household plus anyone else who happens to be hanging around at the moment.
It’s socially unacceptable to invite someone to a wedding without inviting spouse, children, and any other member of the household, including long-term guests.
Of course, catering in India is done in huge volumes. You’d never run out of food if you have a competent caterer and guests eat in shifts if there aren’t enough seats for everyone to dine simultaneously.
1.) This isn’t Asia and 2.) the OP didn’t say that the couple were Asian either, just that they were having a Chinese buffet.
He can ask through a mutual friend, but just assuming she’s invited is, quite frankly, being an ass. Weddings are expensive, and it’s not fair to burden the couple just because you don’t want to attend alone. If that’s the case, politely decline.
Don't say Asians don't think like that when you mean Indians don't think like that. Chinese invitations usually include the entire nuclear family , but not always guests or household members that have no connection to people getting married. IOW , if my husband's cousin is getting married , the invitation will include me, my husband and our adult children who live with us. If one of them is engaged, it would include the fiance. It would not include my mother or my husband's best friend simply because they were living with us for a while.
Chinese banquets are not eaten in shifts.Shifts don’t work when all that speech-making ( not dancing) is going on. Everyone eats at once and the food is served family style to tables of 10 or so. If extra people show up, and two or three people sit at a table for ten, the host is getting charged just as much for that table as they are charged for the tables with 10 people.
And again- just because they’re having a Chinese banquet doesn’t mean they’re using Chinese etiquette. My half-Chinese daughter will very likely have a modified Chinese banquet for her wedding - but I’m certain she’ll be using American etiquette for the invitations and such , since there is only one Chinese- American parent between the two of them.
Maybe ask the best man to ask the groom about the invitation in some sort of generic way. Like, “are Joe and his girlfriend going to be able to make it to the wedding?” It cold be an oversight or it could be that it’s a very small wedding and not couple oriented. If you stay home it could be awkward between the you and the couple in the future.