Hawk seems to be getting slower by the week so having Matthews in the middle certainly helps in coverage and pursuit. Capers letting him freelance in the box seemed to energize him; he showed some of the old special sauce when moving back to the edge against Bushrod; that head fake inside/burst outside sack was a work of art.
That said, I think it's premature to call his move inside a "cure". Once the surprise and novelty wear off, some tape of this stuff accumulates, and the opponent has a QB who has not lost his team, the results are not likely to be so impressive.
Whether we should call Matthews' run defense from the middle a series of run blitzes by design or impatience from inexperience into the wrong gap, more focused and polished offenses can exploit that. The fact the Bears had to play aerial catch-up so early also helped cover some sins in Matthews run defense.
Changing position does not recreate the player. Matthews strength in the run game has always been from the backside and in pursuit. Nobody would confuse him with a stout presence at the point of attack, working off blocks into a hole. I don't believe the days of giving up 150 yds. between the tackles are quite over. He no doubt shores up the pass D in the short zones when he's not edge rushing; that's clearly a double edge sword. Having him in the middle is a good look when the Packers are front running.
One thing I saw that really impressed me that seemed to get lost in all the pyrotechnics was a play where Matthews signaled Hawk to move right; the Bears ran a swing pass to that side. He's not just a pretty face out there.
We'll have to see where this goes, but it might have been a move to contain Forte with pursuit to the edges and in the pass game as much as anything else. In any case, Capers made a good move for this game and found a new arrow in his quiver for certain match ups and situations.