Don't know if this will help anyone but installing from the .msi alone didn't help me. It would install it, but I could not run the app. It would still say something went wrong when launching the app. What I had to do was go into C:\Program Files\Electronic Arts\EA Desktop\EA Desktop and run EABackgroundService.exe. It gave me and error saying it failed but I noticed it created a new folder and changed the current one to outdatedEADesktop. So go back into the new EA Desktop folder that was created and run the EALauncher. It let me sign in but gave an error saying it couldn't connect to the server. For me it prompted to restart the app, and that worked to get everything running.
What an absolute nightmare to get a required launcher installed. Origin would at least work. If the team is this incompetent, that they can't make a working installer, then they shouldn't be requiring it to run their games.