Computer switch

If I start using another computer, because I don’t have access to the one I previously used, could I use the same Alpha Access key or would I have to wait for the steam Alpha Access in order to go back into it.

I think you need to wait until the Steam alpha, unless you had not used your Alpha key previously.

I had already used it.

You might be able to transfer the .exe onto the other computer and play it.

Use a thumb drive

I’d honestly wait until the Steam alpha anyway. Not much you can do in the current version and the Steamworks edition will be much easier and stable (as a platform).