Nothing stops him from pitching hitting, there are plenty of opportunities for that in the NL too.
Does "2 Way" require him to play in the field on his non-pitching days? I don't think that definition is clear.
Someone that makes a cameo appearance pinch hitting twice a week doesn't count as a two way player imo.
The extent that this has drug on is a little silly though. If you want to your definition of pinch hitter to be making a pinch hitting appearance then so be it.
With the game trending from 11 to 12 and now 13 pitchers, there are fewer opportunities to have a one and done pinch hitter in the NL. He'll have to be able to field a position, which Otani doesn't, I believe.
Some AL team, the Yankees I would bet, will give him the DH spot, let him try to use the short porch, then carry essentially a 26th man for platooning with Hicks or wheover else.
He can play OF.