Since posting the story about podracing in the nightclub scene, we've received a couple of comments about the "droid football" game also seen. Here's Jedisaber's report:

You asked the question "When will we see Star Wars Droid Football?" The football game in the Club looks almost exactly like the players and concept in the Video game Cyberball made by Atari. It was a 4 player stand up video game and also was made for the Sega Genesis. The FLO robot in Dex's Diner also looked a lot like the defensive backs in Cyberball.

And there's this corroboration from Eponymoss:

Speaking of the droid football game in AOTC. It sure reminded me of the old stand up arcade game "Cyber-Ball." It was really popular in the late 80's (I myself spent a small fortune playing full games with my friends) I wonder if there's any connection?

Well, Atari did make that classic stand-up of the Death Star attack almost 20 years ago. Maybe this is a nice "tip o' the hat" back to Atari from Lucasfilm.

UPDATE: Sompeetalay has some info about our mystery sport:

The picture in the middle in the Outlander club is not Droid Football, but Nuna-Ball. You can clearly see the Droid throw the unlucky Nuna. There is an article about this sport on HoloNetNews. Worth to check it out :)