I tend to be of the opinion that making relationship agreements about emotions is generally a bad idea; my observation is that most people who do such a thing wind up bitten on the ass by it. (If someone were to ask me for advice on making such a commitment, I would tell them it is ill-advised.)
Infidelity is breaking faith; it’s going against whatever’s in one’s relationship commitments. I don’t think it’s possible to answer the question of what is betrayal without knowing what the other people’s commitments are; further, I think that a lot of damage is done to relationships by people presuming that their partners share their cultural basis for what having a relationship automatically entails, relationship-wise. Sometimes people get lucky and actually did share the same culture; more often, someone does something that’s entirely acceptable within their cultural background and someone else feels betrayed by it.
Someone who comes to a relationship with the cultural belief that “relationship” = “emotional exclusivity” may well feel that they are being unfaithful in fantasising about or caring for someone else. Someone who comes to a relationship with the cultural belief that emotions are okay, just “doing something about it” isn’t may be shocked that their affection is considered infidelity; someone who thinks that “infidelity” requires “having sex” may get blindsided by someone’s claim of betrayal over having lunch with an attractive coworker. In my relationship system, “infidelity” requires “having sex without using a condom or other appropriate barrier protection” or “not telling me about it”.
(And I want my husband to come home so we can go out and hang with his local girlfriend and her partner. )