Windows 10: All of a sudden I can't run some apps with my admin account?

You have already created a new user account. Change that to an admin account and from now on use it instead of the "alleged" built-in admin account.
I still don't believe you have been using the built-in admin, It does NOT get enabled by itself.
But if you really do, leave it alone. Don't use it unless you are in emergency.

 

I think you misunderstand.

Yes, I have already created a new account; I wasn't referring to a third account. I already tried making the new account an administrator and after doing so I receive the same error about the built-in administrator account. Presumably every account that I give administrator privileges will have the same problem. I suggest that the error message is wrong and that this has nothing to do with the built-in account which is probably actually still disabled.

 

The problem was fixed by doing a "repair install". Thanks for your help.

 

Thanks for reporting back on the solution. Create a restore point and a system backup so that you can recover quickly if it ever happens again.

 

That proves you were NOT using the built-in Admin Account because built-in admin cannot open Modern apps.

excerpt: Source
Please be informed that Modern Apps do not run on the built in admin account. You need to create a new account and set it as admin if you want to run these apps as administrator. This feature is by design, made for security reasons.

Please make sure of the followings :
1. Create another admin account for emergency.
2. Get an external hard drive and do system Image backup regularly and save it to the ext hdd. That will save you a lot of heartache. I had used it many times to restore my computer when I had problems I could not fix.
3. Create system restore points regularly.