Security Id's for "Program Files" folders?

I had a strange thing happen to me yesterday that got me to
investigating. One of my game programs, which I had just finished
playing with a couple hours before, refused to start telling me that I
did not have permission to start that program.

I went to the program files folder to look at the security tab. It was
true, my User Id (an Administrator) was not in the list of user names.
I was able to add it, but that got me looking around and there are
dozens of folders out there just like it. Some have my user id others
do not.

Then I looked at the "Program Files" folder itself. I was not in the
user names list there either. But here I COULD NOT add my user id as
the "Add..." button was disabled.

Surely my own user id should be on this list? The "Administrators" and
"Users" names are there among others, but not mine.

Is there are problem here?
Does my User Id need to be added to folders like these?
The only way to do that would be to log in with the "Administrator" Id.
But how to I get access to to enter that User Id and what is the password?

Thanks,

Richard..