I currently play DotA 2 and in the summer my Internet will be capped at 5GB/month. On average how much data does a game of DotA 2 use?
Take care that Dota 2 traffic is not the only thing you should take into account. There are weekly Dota 2 patches (200-500MB), there are Steam patches and Steam traffic.
But speaking about Dota 2 client traffic only, I just measured a single match of 40 minutes and here are the results: