Right clicking and selecting "run as administrator" should have let the program install properly.

That you had to create a new administrative account, points to a problem with the original user account you used.

The fact that you created the "admin" account as an administrator is co-incidental, nor is it really necessary, though it was a good move.

In your shoes I'd save the files from your normal user account, then delete that account, reboot and recreate it, and finally copy local user files back.

Otherwise whatever hung up Realflight is likely to rear it's head again with some other program in the future.