“Center of the table” doesn’t mean all jumbled up. It’s possible (probable?) that the drinks were arranged according to who ordered what, but were towards the center so that the plates could be set in front of everybody. This makes the most sense to me, especially if the table was on the small side.
Or “giving a white russian to a toddler”
Side note: You wouldn’t believe how often I’ve been able to use, “It was like taking tabasco from a baby” in conversation lately. 
We’re all overlooking a major point in this story:
Who the fuck orders a White Russian when you’re having Chinese for dinner? Blegh!
The Dude, among others. It’s a very tasty drink. 
There are many things in the history books that make a whole lot more sense to me if I assume everyone was drunk.
I thought that was illegal?!
Yeah, what ever happened to “Never get involved in a land war in Asia?”