Hello,
I just purchased a subscription to use with HearthRanger and also encountered this issue.
I have it set to play Casual/Wild play mode. It selects the appropriate game mode, selects the appropriate deck, but doesn't seem to actually start the match. I can see it looping through the same clicking action but nothing happens. If I manually click the Play button to start the match, it works fine up until it gets back to the Play screen again.
I've tried restarting both Hearthstone and Hearthranger - and also starting them in different orders but the same issue persists. Could it be related to the windowed dimensions? My dimensions (under Options) shows blank - I recall making some changes to increase the FPS and set Hearthstone for 4K display. The game is in windowed mode.