Ah, that turn of the 20th century humor!
I'm thinking he may have been part of a team of large guys. A team with everyone over say 300 would probably have done very well if they played for a portion of the gate.
There were a few things like this, the bloomer girls in baseball, and even fat guy bicycle races as part of the program at some velodromes.
This page has an ad card for one of the competitors.
http://mlkshk.com/p/DBTU
Sadly there's not much information out there about either the races or the racers. They must have been at least somewhat athletic since most indoor tracks were very steeply banked and often required a certain speed just to stay on the curve and not fall. Maybe as much as 20 Mph which would be simply amazing for someone as large as Grimes.
I'd bet the ballplayer shown on the postcard wasn't half bad, just oversized.
Steve B