Hi Bernard,
Whether the 70-200 f/2.8 IS lens is suitable for your indoor shoot would depends on the lighting conditions. The 70-200 f/2.8 IS lens is 1 stop faster than the f/4 version and basically it means that at wide open, you would be able to achieve half the exposure time compared to the f/4. ( ie 1/30s at f/.8 vs 1/15s at f/4)
Perhaps you would like to examine the past photos that you have taken and note the average shutter speeds of the pictures taken during the indoor shoots. Say, if you are consistently getting 1/30s exposure time with the f/4 at cameras max ISO during the shoot, you will probably be getting 1/60s for the f/2.8. Is this fast enough for you?
However if you are getting 1/8s with your f/4, the f/2.8 will give you exposure times of 1/15s, which IMO is just as bad. In this case, lens like the 85mm f/1.8 or the 135mm f/2 might fare better. Even though, under this type of circumstances, you might just be able to take momentary stationary shots
If you really insist on catching all the actions and smashes in the game under lousy light conditions, the fastest glass available for canon would be the 35mm f/1.4 (too wide), 50mm f/1.4 (too soft wide open), 85mm f/1.2( too slow in auto-focusing) and the 200 f/1.8 (too hard to find).
Hope it helps.
;p