Installing the game is simple enough. Just download the latest installer (it's pretty hefty) then fire up a terminal and run it:
~$ sh ./HoNClient-2.1.10.sh
You don't even need root access. In fact, the installer will tell you to run without root access if you attempt it. Nice.
The game even starts up without any apparent errors.
Unfortunately, it lags too much to be playable. Just the login screen lags horribly. I didn't bother trying to start a game.
Maybe when Precise Pangolin is out come April 2012, we'll see if things got any better. The open source driver in Ubuntu 11.10 doesn't have the latest improvements and it's supposed to be much better now.