Can I run with a computer in my backpack?

There is always some risk when doing anything with your laptop. As long as your only drive is the SSD then it should be rock solid.

Optical drives wouldn’t like this kind of shock so much but will actually survive fairly well (I’m basing this on the fact that 20 years ago I owned a Discman which I used for running).

I believe that the laptop you are using uses LED backlighting. If this is the case then it should be fairly shock resistant. Unless I’m missing something, it should be fairly safe. But be careful with it though. don’t let other objects in your backpack crush it. Breaking the screen is really the main concern I would have.