Im making a project proposal for a game whose gameplay involves endless road where player just has to dodge obstacles but it also has time limit. Its as if temple run but can only be played for certain time limit and you have to make as high score as possible within that time. Temple run can be called as "endless runner" game but if it had time what would it be called. I want to know how would you describe this game type in one or two words? As in "first-person-shooter" or "Racing" etc??
According to some definitions, an "endless runner" is a game that requires forward motion at all time.
Thus it requires only that the player can't stop moving; i.e., that the motion does not end. It does not require that the game itself does not end.
So your game would be an endless runner if the player is forced to keep moving, irrespective of the duration or whether the end of the game/level is based on a timer or a certain distance travelled (and, in fact, these would be the same thing in most "endless runners", as the player usually move along at the same speed).