Do rat terriers play tug?

Ok, so I am reading in Natural Dog Training that a dog needs to get the bite out. Our terrier will have NOTHING to do with any tug toy, not matter how much I wiggle, try to tease, get him to chase, as soon as he realizes there is no actual food involved - it is over and there is ZERO interest. If I use an actual edible chew bone...he's all game though, but Stormy the rat terrier will not bite any tug toy, let alone play tug.

So I am left with only pushing and the associated feeding? Not that pushing has not had good results, and this is only week 4, but what about the tug and getting the bite out? Does he not need that?

Mind you, this dog has caught many a rat. Their success was greatest while Skye lived with us - rats, moles, and a squirrel. Sometimes, when Skye caught a rodent, she would not kill it. Once I found her playing with a mole who looked to be unharmed and I carried it off to a save spot and I think it got away. But every now and then I found a young rat still breathing but "playing dead", or not dead yet but possibly hurt, I would call Storm the rat terrier over and: "crack" one bite to the neck and it was dead. Thinking about it now - his way of hunting does not involve a lot of tugging on a large animal....They were busy for hours on wood piles or on the ground sniffing and digging for those little critters - then a quick bite and ...dead. He HAS on occasion eaten his prey.
In fact, they both went nuts over rodent noises in tree trunks, wood piles or in the ground, sometime staying on it for several hours. Their passion for hunting really is what bonded them and allowed them to be such good friends imo. They were ..."happy" for lack of a better word, and in a way it was such a pleasure to see them like that.

Anyway, back to trying to get Storm to play tug. So I remembered that during the 6 months we had Skye, our German shepherd husky, he watched her tug, and play fetch a ball, except she'd tease me, not always bringing it back to me but run off with it with excitement or bringing it to the other dogs  - and he saw her get an occasional treat. He even started to get interested in running after a tennis ball himself....looking really cute...and I gave him a treat too at times.

So the other day, after unsuccessful attempts with  "tuggable" things last week, I started working with a tennis ball and HE REMEMBERED. He ran after it and quickly learned that when he picks it up in his mouth - he'll get a treat. We have only been doing this on 3 different occasions and it looks like he is getting really interested in catching the ball with a quick bite then drop it. Today he looked like he would eventually want to grab it out of my hand...will this be the beginning of tug?

Will he eventually enjoy it without getting a treat - at least without getting a treat each time?
Maybe rat terriers don't play tug like the bigger prey driven dogs?
And what if he had never seen the other dog play with the ball?
Is it really that important for him to bite?
Does he really have to play tug? (not that I don't want him to)

I'll keep you posted. Pictures and video coming - but it has been a little busy lately. And if there are any natural dog training enthusiasts out there with answers, please, I'd be delighted.....