No, it's not trying to install anything extra; it's just Windows being overly cautious. It's what's know as User Account Control (UAC). If you trust all the programs you have installed, you can just change the UAC setting to a less restrictive one (or turn it off altogether, as many people do). This can be done in the Windows Control Panel.

The alternative is disabling the "Run as Administrator" option in the Properties for whichever individual programs you want to do this in. (Some games work better when run as Administrator, though, which is part of the reason why most GOG installers set them up that way; I've played SPAZ with that option turned off, though, and it worked fine for me in Windows 8.1). If you want to turn off the "Run as Administrator" option:
- Right-click on the game icon
- Click "Properties" (at the bottom of the menu)
- Click the "Compatibility" tab at the top of the Properties panel
- Look for a check box near the bottom that should say something like "Run this program as an administrator", and make sure the box is unchecked
-Click "OK"

Unless Windows 7 treats this game differently than Windows 8 does, that should get it to stop bothering you with that notice every time you try to run SPAZ. Note that you can try this with other programs, too, but, like I said, some games don't work quite right unless they're run as Administrator. (Also, I've got one or two games that still give the "Unknown publisher is trying to make changes to this computer" message even when the game is not being run as Administrator, so....)