Here's one way that you can try and remove the Google Play Services dependency using Lucky Patcher. Install lucky patcher (a simple search should give you it), give it root permissions, and then you can do one of the following next:
- Create a modified APK file which has the dependency removed
- Or directly patch the app
Creating a modified APK file
Open up Lucky Patcher. Find the app you want to patch, tap on it, and select Open Menu of Patches. Select Create a modified APK file, then APK without licence verification. Near the bottom of the list there should be an option labelled Remove dependencies. Make sure that only it is checked (ie: all others are unchecked), and then select Rebuild the app at the bottom of the dialog. Wait until it's finished (it may take a while), and voilà, you'll have an APK which shouldn't require Google Play Services. With this method, chances are you'll have to uninstall and reinstall the app with the custom APK, thus loosing all data (unless you somehow back it up).
Directly patching the app
This method is (probably) simpler and doesn't require you to uninstall or reinstall anything. First, if your app has been moved to the SD card through the normal method through settings, move it back to internal storage. Next, open up Lucky Patcher like the above instructions, and find your app. Tap on it, select Open Menu of Patches, then select Remove licence verification. You'll want Auto Modes here, so select that. Now check the Remove dependencies box and make sure any others are unchecked (however, if you want to, you can select Backup APK file in case something goes wrong, because then you'll have something to revert to). Select apply, wait for it to finish (again, it might take a while), and there you go, you should be done.