Does the game really restart after 90 minutes?
No, you won't have to start over. When the time is up, you can continue as if nothing happened. Completing the game in under 90 minutes is an optional bonus challenge you can take once you completed the game at a leisure pace.
Unless, of course, you think you are REALLY smart.
For completeness, here is the only thing that happens when time runs out:
(potential spoiler, hover over to see image)