I could see mixing them up at hatch, if one didn't look at the feet, and depending on what color of Old English Games. Some of them have down colors that are similar to what Light Brahmas have, and all kinds of combs are really tiny at hatch.
(But if I knew I had Brahma bantams and OEGs in the...
Old English Games come in so many colors it can be hard to know for sure whether you've got a rare color or a different breed (although that color is very common in Brahmas, and rare in other breeds.) And of course the feet are really distinctive, once you know to look for them :)
Old English Game Bantams do not have feathered feet. Brahmas do.
Old English Game Bantams have single combs, Brahmas have pea combs.
So there's two things you can check if you have to deal with that breeder again ;)