Can I make a game with speaking hamsters? (and if so can I include Bob in it)?
James does not own the concept of talking hamsters. Talking hamsters are too generic to be a trademark. Even a Hamster named Bob is pretty generic.
As it happens, Bob the Hamster is the eldest of 144 children, all of whom are also named "Bob", even the sisters. Bob's mother thought this would keep things simple, so she would only have to remember one name, but in the long term, it just caused confusion.
If your game contains a hamster named Bob, it is entirely possible that it is one of Bob's brothers or sisters.
If you want the Bob the Hamster to make a cameo appearance in your game, you can consider it fan-fiction