Is there a way I can transfer my in game purchases from what I purchased on mobile over to my PC?
That's not possible sorry. Only possible if you're using the same platform. I suspect once they implement an account system this should be possible but at the current state nope.
This only works if you're using the same account i.e when you get a new phone simply using the same playstore account as you did in your previous device, if you're on a new computer use the same steam account as your previous computer, on your new iOS use the same app store account as your previous iOS device and you'll always have your purchases with you.
That's the only way for the meantime.