There were a few reports recently from origin users, not sure yet why it happens though. It seems like EA changed something...
Can you please go into your game folder and look for the file "ra95.exe":
Right click -> Properties -> Compatibility: Disable everything in there and try to start the game again
Actually I updated RA1Installer with a possible workaround a few hours ago, when did you download RA1Installer?
I downloaded the installer a couple of hours back.
I tried your suggestion about disabling compatibility and it worked!
I'm going to re-download the installer one more time to make sure I have the latest version just in case.
Thanks for your help!