I reject the entire paradigm offered in that the three types all refer to combat only, particularly in manipulating rules for benefit (rules-play). If there's something for rules structure to be learned from another game, I'm for it, but not to put the entire "crunch" of the game into combat.
The only "type" offered that has something to offer is Timmy, who possibly represents that in-game improvisation that is at the heart of real role-playing games.
Let's borrow concepts that will allow participants to act in a way that the rules "fade into the background" in the light of free flowing play at the table.
That's right, the entire MtG paradigm as presented is more-or-less limited to combat only. Therefore, in pondering how MtG could influence D&D we can take inspiration from its combat and the paradigms which that game seems to serve reasonably well. (If you like, call Timmy, Johnny, and Spike "aspects" of players: precisely the aspect that interacts with crunch.) None of this necessarily conflicts with the existing or future scope of D&D. If that's the case, I don't see the need for

In fact, it is entirely possible to borrow concepts from MtG that might allow the rules to fade away. For example, the stack/"interrupt" nature of MtG might inspire a system that describes dramatic action with some form of renewable drama point, where spending these allows one to interrupt the description of the narrative such that more recent modifications always have precedence, until we determine what really happened. This could be extremely light, diceless, applicable to more than just combat, and still be influenced/inspired by MtG. How would this not meet your criteria?
Your characterization of the "heart of real role-playing games" as one of improvisation is at best incomplete, unless we're using a very broad definition of improvisation. I object to the use of "real" since it allows anyone, without a moment's thought, to label any characterization of role-playing they don't agree with under the "not real" category. It is an invitation for No True Scotsman at its finest. (I am not suggesting you would necessarily do this.) Rather than get into the age-old argument of what an RPG is, please allow for the possibility that a crunch-heavy and, yes, combat-heavy game can be a method of immersion. That is, at least, in keeping with the reported experience of some players. If you wouldn't want to play in such a game, I can hardly object. Play whatever game suits you.