It seems that at least some versions of SBB Mobile are depending on the Google Mobile Services.
You could try to install SBB Preview, perhaps this will work without GMS. I have read that it works with microG, an open GMS replacement. This could also be worth a try.
The developers should not depend on GMS, the app should be able to run on all devices. The compatibility page on sbb.ch states that it needs at least Android 5.0, it does not say anything about GMS.