You are right, your son’s glove side looks “soft”. Not to fret, because many, many beginning youth pitchers have the same glove-side issue. Throughout my son’s LL years, I also noticed that a very large number of dad-coaches were unaware that the glove-side is even important.
Of those who were aware that the glove-side is important, many (most?) believed that pitchers need to “pull the glove into the body” during launch of the baseball.
Unfortunately, at the typical speed of a pitching motion “pulling the glove in” before release of the ball looks pretty similar to what the majority of elite pitchers really do–they swivel the glove into place–somewhere out front generally above the stride foot–and stabilize it there while their torso tracks forward to meet the glove.
Although “tuck the glove into the body” and “swivel, stabilize, and bring your body to the glove” do look somewhat similar…they have different consequences. Guys who stabilize their glove out front and bring the torso forward to meet it are directing all of their momentum forward to the target.
Guys who “pull the glove into the body” before release are splitting their momentum between the target and the direction their glove side is going. There is no question that pitchers can compensate for this inefficiency, but (IMO) once this habit is deeply ingrained it will be exceedingly hard to change and it won’t carry a pitcher much beyond High School, even if he is otherwise very sound.
Your son is lucky because at 9 yo he can easily change from his current “soft” glove to an effficient “swivel and stabilize, bring the chest forward to meet the glove” mechanic.
I’ve seen Tom House teach this to kids many times: He watches kids throw for awhile, then he asks them to stop and he shows them in slow motion what it means to swivel the glove into place, stabilize it, and track forward to meet it with the chest. Then he asks them to throw with their normal mechanics but on every subsequent throw he wants them to make sure they keep the glove up and out in front as they launch the ball and follow through. He often asks them to keep the glove at the height of their chin so they will definitely feel different from their old habits as they track forward to the target. Kids that back-slide into their old “soft-glove” or “pull the glove in” habits are reminded to do correct repetitions until “swivel and stabilize” feels comfortable and normal.