Games have many different ways of dealing with mental stress. Many just ignore it, and rely on players roleplaying such things, if they so inclined. Call of Cthulhu goes to the other extreme and makes mental stress not merely a mechanic, but arguably the single defining mechanic of the whole game. And there are other games in between, where heroes can suffer various ill effects when confronted with situations that may mentally drain them.
An option is for the GM to enforce some forms of mental strain essentially by fiat, at appropriate moments when the character actions or circumstances make it sensible to assign or interpret events as being stressful. Perhaps that's what our GM has done here when Pete said he was fleeing.
Commentary by memnarch (who has not seen the movie)
Mental recovery to stop running too much? I guess that works. Rey didn't seem that mentally out of it, but maybe it's a save to avoid running until she gets another Fatigue point. Fatigue never seemed to be an issue before this Episode though; I wonder if this is a new detail to keep things interesting for movie-watchers or if this is going to boomerang back at some point as an explanation for something coming up.
I don't know if I'd call a sphere perfect for all terrain (cough climbing cough), but BB-8's definitely a lot better at moving around than R2-D2 was. Personally, I think a properly built walking robot would be more practical and maneuverable, but! This is Star Wars: practicality takes second (or fourth) seat to looking cool. Bipedal walking robots with tool dispensers on the sides? Pretty cool. Ball rolling robots with tool dispensers across the whole ball surface? Very cool.
Commentary by Keybounce (who has not seen the movie)
[Keybounce's comments will appear here when received.]
GM: Rey, you’re running at top speed through the forest. The tall green canopy bathes you in a cooling shade.
GM: Make a mental recovery roll at +3.
GM: You realise you’re out of breath. You stop to gather yourself.
BB-8: Are we done now?
Rey: How did you get here?
BB-8: Sphere. The perfect shape for any terrain. How did you get here without tripping over a root and faceplanting?
Rey: I’ll allow it.
GM: You mean I’ll allow it.
Rey: Oh, the game can be under your control, but not mine?
GM: That is generally how it’s supposed to work.