The TE should be fine for games.
I play games using my Kinesis no problem, have played WoW on it for years, now I'm more into StarCraft 2 and Skyrim. The TE defaults to the same switches as the Kinesis (brown), which should work fine. Last year I switched to cherry reds: bought a full LF (red) Kinesis as well as red key wells to convert a brown Kinesis. Sadly I forgot to convert the TE I had on order to red switches, so I have one with browns. The difference is small but noticeable, but either should work fine for games. At work I use the Kinesis with reds for programming, which works well too, so personally I'd get red switches no matter what you do, but that's just my preference. As others mentioned TE recommends reds for gaming only.
About gaming on split keyboards: with any split keyboard you will want to avoid having to use keys on the right half of the keyboard, because they're so far away. So in WoW I had to make do with just the left side. I ended up with three layers of a key grid 5 keys wide and 4 keys high, the top layer (no modifier), the second layer with Ctrl pressed, and the third layer with Alt pressed. On the Kinesis Ctrl and Alt are easily reached with the thumb, on the TE you might be comfortable hitting Ctrl with your pinky - personally I'm a thumb-modifier person and would want to remap the left space key to some modifier (probably Command/Ctrl). Anyway, on the TE I'd probably have used Shift as modifier for the third layer.