I don’t know if the Companion needs Google Play services.
But you can download the Apk from your Project and Sideload it with adb. Maybe it’s even possible to install apps from unknown sources and install it directly from your tablet storage.
Some Guide from Google for install an Apk File:
Start installing the APK.
If the installation window appears with a grayed-out button, put the tablet into standby.
Bring the tablet back out of standby.
The installation button should now be active and can be used.
Be happy about the APK that has just been installed.