Thumb under the tongue when the dog bites you and say nothing. Let go when the pup settles a bit, otherwise if it's attached to you scruff it.
Mouthing and bite inhibition is not a game, it's a serious matter that needs to be dealt with swiftly and not tolerated at all. As for staffords mouthing, no it's not a breed thing you cannot train out of them you just need to make the lesson stick and from a young age. You put your thumb under the tongue and press gently, just hold on despite the kicking and screaming they put on to get one up on you. Offer your hand again if the dog licks, treat and praise. No dog in this house, big or small, will ever bite my hand because they learned early teeth on people is not acceptable. The only time I have not done it is with working dogs, they get prised off you and onto a bite toy - but then we don't want them to learn never putting teeth on a human is bad.
And just some things on tug of war games
1) you do not put your hands in to extract the toy from the dogs mouth, offer another toy to the dog as a swap. Keeps the grip good and down the track, if IPO/Schutzhund and protection are your thing, the dog will not let go at a hand on its muzzle which you can inadvertantly teach. This also makes the game fair to the dog and they quickly relinquish the item in their mouths because it is not a LOSS it is a SWAP = WIN. You add the command to release when the dog understands the game.
2) you do not do a lot of tugging with teething pups, and you NEVER lift them off the ground/spin them. They can rip off teeth and injure their mouths, which in turn can ruin the whole tug of war/toy reward process, conversely they can injure necks/jaw
I have a car load of the prey driven, arm tugging buggers trust me I talk from experience