I restarted my computer and that allowed me to delete the temporary files from Local.
Went through the command prompt and deleted the folder from regedit.
Deleted from AppData/LocalLow/GameLabs.
Installed the launcher and this time unchecked the box to have it launch automatically, for good luck.
Double clicked on the desktop shortcut and got back to the login screen, so that's progress!
Successfully remembered my login info and got to the screen with the ships on it.
This time I did not check the box to have it put a shortcut on my start menu, but I got a notification that I can find the launcher in my system tray, so maybe that was my problem from the start?
Game finished installing, hit play and got started just fine. Closed the window so now we'll see if the problem starts again.
Double clicked on my desktop shortcut and got the game started again so I think that did it!
Just tried it again and the error came up but then it worked anyway.