Does installing/running Blender tamper in any way with my system/settings or install additional software/required components? My question is, does using Blender (since it doesn't require an installation as far as I understand) tamper in any way with my system, install additional/required/third party software or make any long lasting changes to my registry?

I'm using Windows 8.1 64bit with all the current updates at the moment.
No it doesn't modify your system, provided you are using the self-contained .zip version.

The self-contained .zip version is just that, self-contained. It will - of course - put data where-ever you tell it to. Animation output or other temporary files will be written where you tell Blender to put them. Temporary files (in C:\tmp\ by default) are deleted every so often.

In addition to the outputs mentioned above, the Blender Windows Installer will also make a link in you start menu, (possibly) on you desktop and will associate .blend files with the Blender executable. This file association is done via the registry but should be harmless.