The question is that everything used to work fine for him, so a lack of resources can be ruled out. Judging by the symptoms, the graphics card is malfunctioning. If installing drivers doesn't help, it might be a hardware issue. I would suggest checking the graphics card's temperature under load if possible.
The thing is, the other games don't have these issues (even with higher requirements than Heroes)... and it definitely isn't related to DirectX, right?... Moreover, it's not just glitches; there are also lags, like complete freezes. That's why I thought about some kind of system error....
Added 1 minute ago
Try updating Heroes to version 3.1. The patch is available in our HeroesWorld file archive: /files/10078/>
Sorry... I didn't notice that. I'll try it now and let you know the result.
Added 1 hour 48 minutes ago
And how can I check the graphics card's temperature? Because I'm starting to suspect that too, since these lags are gradually increasing from the moment the game starts.