Scott you might want to try that on the same course and hole. I know if I am gleaning credits on mobile and then start playing a game on the PC launcher, it causes all kinds of problems. mobile and Launcher(PC), same account. Have forgotten and had to withdraw from a number of games because of it(I just flat cannot play on the small screen on mobile.)
What you show above, is on the left, is St. Andrews, on the right, is Wolf Creek, plus you are using the same account for both. We don't even want to go there about the other way(2 accounts) Did you even try playing. I can start a game off of the launcher, with the mobile running also, but after the first couple of shots it starts asking if I want to resume/forfeit on each shot on both screens, I end up having to forfeit the game to be able to get out of each device. Once you forfeit on one, the game is gone on the other. (this might be an indication as to why WGT seems to be having problems with cross platform play)
I don't believe what the OP is trying to do is possible, without taking the chance of getting either 1 or both accounts banned. 2 computers, 2 accounts same household, I know is possible. Playing against each other, depends on game, might be frowned on.