"Run as Administration" option won't work for Flash Player

So I'm using a friend's laptop, and it doesn't have the required Adobe Flash Player to run one of my games.

I downloaded it, and it shows in my folder, but whenever I click "Open" or "Run as Administrator" nothing happens. I've tried re-downloading it, checking my programs, googling help, and nothing helped.

I made this account as an Administrator today, but there isn't any errors that pop up saying I'm not an Admin, or any errors for that fact.

I'm getting quite annoyed... I just want to play my game. I have absolutely no idea why nothing will register, and why it won't let me install it. I've installed this multiple times on other computers and I've never had this problem.

Can anybody help me, please? I'm all out of options.

Edit: Well, apparently it's necessary for most of my websites... so PLEASE someone help!