The "game" part seems to have been bred out of Old English Game Bantams pretty thoroughly, at least as regards the ones sold by hatcheries. I've noticed some hatcheries are now calling them "Old English Bantam" and leaving out the word "game," although I can't tell if that is because they care what it means, or just an effort to make it shorter.I had heard they could be feisty due to game birds being used for fighting, etc, but she's not at all.
I haven't seen them being any worse than other breeds in a flock.
I have had a number of bantam Easter Eggers with chipmunk stripes, although they were ordered from various hatcheries instead of picked from the bantam bin at a store. I think Ideal and Dunlap were the ones I ordered from. Some in each batch of EE chicks had chipmunk stripes and some did not.I think in the bantam bin, it's safe to assume any chick with chipmunk stripes is an OEGB.... I think bantam EEs can have it too, and Hoover's has those. So maybe that's not actually a safe assumption, lol.