It isn't necessarily Schelling, escalating conflict by taking us down his metaphorical slope towards inevitable destruction. Maybe, but at this point, there is a far less dangerous explanation. Here's the basic problem in game theory. Not everything is a perfect information game.
Consider the game of "chicken." We're going to keep coming back to this one. Two people drive towards each other. If someone swerves, that driver is a chicken. He loses. If nobody swerves, um, oops! Crash. If the cars are going fast enough, both drivers die. If both drivers swerve, they're both chickens. At least they don't both die. How do they each rank the various outcomes?
(a) death < swerving alone < both swerve < winning
Figuring out a decision requires trying to figure out what the other player will do. The problem is that not all players are the same type, and you may not know what type of player you are facing. There may be some player types who are less concerned with dying. Would you play this stupid, adolescent game?! There may be some whose egos are so fucking massive, or at least fragile [cough, cough, Trump] that they might actually rather die than be seen as a loser. (Then again, he was a draft-dodger, so...). In that case, there may be some players with the following preference ordering:
(b) swerving alone < death < both swerve < winning
If you don't know whether you are facing someone with ranking (a) or ranking (b), you've got a real problem. How do you deal with that? You might want to play some low-stakes rounds to figure it out. You know, where the result of both sides not swerving isn't dying.
A new president was just inaugurated. Other leaders need to feel him up. Out. I mean, feel him out. Trump is an unknown quantity, as new presidents generally are. He is particularly unknown, though, making these kinds of gestures both important and to be expected.
What will he do in response? I have no idea. The fact that we are seeing this, though, is basic game theory.