Yes playing a hard game could be considered HIIT, the only problem is that the other people you play with may care about your fatigue level as the game goes on. If you play all out running after every lose ball being an animal on defense, then you get a "rest" on offense. Incredibly difficult. Me and my buddy used to play games to 11 or so, or time it and whoever was ahead when time ran out won. Very, Very, Very difficult.
I was wearing a heart rate monitor playing New York Ball with 2 other kids and they were like "what is that beeping" My heart rate was maybe the highest I have ever seen it with my watch on. The harder you do this though, it will get to the point where you are so tired you wont even be able to make a shot.