It is made very clear that Dormamu is experiencing the loop at the end of Doctor Strange as a sequence of events, much like the viewer.
Indeed, that's the point - from his perspective he's going to 'live' these moments forever, getting bored and unable to proceed beyond them.
Is Dr Strange experiencing that too? Or is Dr Strange's experience getting reset every time (with the note that he KNOWS conceptually that he is at some arbitrary point in the cycle?)
If he is experiencing it, then how is he planning to not get bored or give up to escape eternal torment? It's made clear that at least some of the deaths hurt. So it seems like he's merely set it up as "I reckon I can be more stubborn than you can" which seems ... less certain.