If you've ever seen a dog gnawing at a bone, he looks like he is trying to eat it, but is incapable of doing so and is possibly struggling, but might be enjoying it. A kind of futility.
In your quote from the World Trigger manga series, Masataka Ninomiya compares Osamu Mikumo to a dog gnawing a bone. Mikuno is nicknamed "four eyes" since he wears glasses which immediately labels him as having low trion. Ninomiya is a superior fighter to Mikumo and his quote is criticizing Mikumo as a "light weight" fighter.
Ninomiya is basically saying that Mikumo will never have a fulfilling "mouthful of strategy" but only "bits and pieces of tactics" for his fighting ability. It also plays into the image of "giving a dog a bone" to keep them quiet while they are preoccupied "gnawing on the bone".