I might also toss in there that anniversaries (any holiday or celebratory event) can be very triggering in itself. H feels that any efforts will fail so he often does not try, or gets very cranky beforehand. He feels pressure and expectations (that I try to never put on him), and that makes him more likely to freak out, to engage in silent treatment, for awkward sex where he complains or picks a fight during - it's a mess.
So, your BF may have been on edge, to begin with - he started the whole weekend off by accusing you of already ruining it by being "inconsistent" and expecting him to "wait all day" when to me it sounded like you were on time. The first part to me sounds like he did not want to deal with it, and the incident with the game was just something to latch onto and ret-con into it all being your fault.
That said, the minute he started with the silent treatment, stop asking him, "what's wrong, what did I do, are you okay?" That just fuels the fire since you can't read his mind and already know like he expects of you - to him it can sound like you are trying prod him even more. His emotions are the only ones he can process and understand, especially one he's allowed himself to get upset. Yours are not even "real" to him, and for some reason, pwBPD tend to believe we hurt them on purpose, that we enjoy causing them to get upset, that we JADE not to diffuse things but in order to purposefully escalate them. Once you see the warning signs, stop. Just stop trying to talk at all is sometimes safest. There are times you can discuss things, in silent treatment mode or rage mode, those are not those times.
He will inevitably take something very personal
^^ Yes. Everything is all about them, and all comments meant to praise or harm them - there is no happenstance, there is no "I didn't know". They are very sensitive to anything that can be perceived even remotely as a slight, and they tend to assume you (or anyone else) did it on purpose, because to them that all makes sense. H comes out of left field, hurt and upset by things that had NOTHING to do with him, that he chose to interpret as being an insult to him. For me, it's all very confusing and hard to tell what happened when he's upset by something that NO ONE meant against him. He is also easily embarrassed and finds reasons to hold onto shame and negative feelings, and then push them off onto me to get rid of them.
Try to remember this person you are with is not fully emotionally functional. Our desire to explain away hurt comes across as a fight. As an excuse. It's never enough to explain, "Oh, you thought I meant something bad about you? But I was talking about a character on TV/at work, etc." It's always how their first emotional knee-jerk reaction made it FEEL, not any truth, logic, or facts, or even your point of view. They have a hard time, once triggered, hearing any of those. I try to no longer waste hours being yelled at while trying to explain how I did not even say the things he is accusing me of, that those are ideas coming out of his own head. Later, calmer, at a time removed from it, you can talk about (hopefully). But during the storm it's best to try to just keep a distance (physically or emotionally) to protect yourself. When you see the silent treatment start, you can't stop the train by standing in front of it - you get off to the side, and look for the brakes. Same with the rage. We WANT to JADE. It's a normal desire to make someone not mad by explaining to them how their interpretation is incorrect and so they should not be mad - but that is invalidating. Invalidation is a form of abandonment to a pwBPD.