i wonder if he's actually playing a game, or just trying to assert personal space. THIS INTJ doesn't like games at all though i don't always express when i'm not getting enough personal space the correct way and just try to get away as best i can instead of creating potential stress or hurt.
it's possible that your SO just isn't empathizing your situation fully. INFJ + INTJ can be a recipe for conflict too as your world is so emotional and ours isn't. talking about feelings just isn't our thing, and as a joke, i came up with this sarcastic reply to potential feelings nags...
"how am i feeling? i'm feeling very annoyed that you have to keep asking me how i'm feeling every 30 seconds to the point i can't hear myself think to even know. that answer your question?"
talking about feelings, even HAVING THEM just isn't part of the INTJ way.
going back and re-reading your post a 2nd time, it could be too that he's trying to avoid the situation entirely. i absolutely dread such conversations, and would try to dodge them myself, not as a game, but because it's just so far out of my understanding. i never know what to say and am very likely to say the wrong thing because emotions are just silly abstractions that get in the way more often than not and there's NEVER a LOGICAL solution to emotions. hugs? OK, now THOSE make sense.
you're just talking a foreign language to your guy. it's quite possible it makes him anxious and feel like he's on the spot. if ANYONE has a gift for blurting the exact opposite of the right thing in an emotional context, it's an INTJ. i wear my TWO "brutal honesty" backhanded compliments with pride as at least i'm consistent there, if totally incapable of telling people what they want to hear.
it's frustrating to WANT to help someone, but knowing you just don't have the tools to do it and are likely to make things worse for trying.
Did you actually say that you wanted him to stop and talk to you about something because it was very important to you, or did you just expect him to automatically assume that he ought to do that? Based on what experience I have with INTJs if you don't outright ask or make known what you are specifically expecting from him, he is likely not going to realize what it is that you are needing from him.
TRUE TRUE TRUE so very very TRUE! oh it drives me nuts when people expect you to have the same grasp of emotions as they do. for the most part, INTJs, at least this one, are very independent and used to handling their problems on their own, or annoying everyone around them by complaining and not liking their emotion based solutions anyways. from our perspective, a lot of human nature amounts to
"what is all the fuss about?" we just don't get it. if it isn't logical, ignore it until it goes away.
being problem solvers, i'd expect a truly involved in their relationship INTJ to WANT to help as best they can when an elusive emotional issue is brought into focus. i liked the poster who mentioned DUTY. that is a word that should resonate with any INTJ who still lives up to the deep commitment trait that many of us share. in the context of "it's your job to offer your shoulder", i think even an INTJ could get that, maybe not an INTP or an aspergers case, but
"it's your duty to go comfort her" makes total sense to me.
OH... by "playing a game" you might have been literal. in that case, yeah INTJs really don't like being interrupted, and when you chose such times instead of free ones, it can drive a wedge for sure. nothing does that better than trying to live up to someone's unrealistic expectations of you to behave just like everyone else. it's times like that that we get labelled as "selfish". i can see where i get that label a little better in this thread as when i'm not pre-occupied, i like to go out of my way to help even strangers, as long as they're nice. if you're also in an agitated mood, that could be part of the reason he's avoiding the situation too.
the best bet is to appeal to INTJ logic, like the "duty" comment. that is a concrete word that can be applied to relationships much better than flowery emotional terms that mean little to us.
i'm feeling some guilt by association here.