So far I have been putting the game away if he freaks (we're talking full-on weeping tantrum) and telling him we can play again later when he's calm. This doesn't seem to be having much effect.
When you say "no effect" - what is his response.
One thing you may want to try is talking BEFORE the game about what to happen if he starts to feel upset. Give him a very specific thing to do - if we start to feel upset we will, stand up, take a deep breath and stretch. If we lose we will say "good game" and shake hands. Role play these activities and then model them in game. Talk through it aloud "I notice I'm getting stressed, I'm going to stand up and breath, please do it with me." If he gets into the habit then when you see when the game is going to take a bad turn you can encourage this. And, of course, really notice when he handling it well.
Also, I will say that personally if I start to see really intense energy around an activity like this I'm okay with talking about how that isn't healthy and letting it go for a bit. For sure I would have limits about how much it is happening particularly with any software. Burn out is a real issue and it is important early on to focus on balance in life.
