Last I checked it didn’t have Battle Mode arenas at all. Not interested in races.

It has a battle mode nowadays (and has for several versions now). Somewhat more recently, they added support for network multiplayer in version 1.0. I recommend you take another look and see how much it's improved if you're still interested.

Also, the engine has gotten a lot fancier, and there are new tracks that take advantage of the engine capabilities pretty well.

Super Tux Kart does have battle mode somewhat similar to the Mario Kart balloon fight though not as polished (and many of the arenas are a little too large in my opinion). It also has a unique soccer mode.