I presume you intentionally don't want Google's services installed?
If so, you could try installing the MicroG framework instead (an open source alternative reimplementation of Google Services, that might be enough to get the app working - no guarantees, though!)
https://microg.org/download.html
Another option is to install the Amazon appstore, and install the version of Moovit that's there (assuming it's the same app) - that version shouldn't need Google Services at all, as it's packaged for Amazon devices that don't have the google services