I would like to install the required plug in to play this game but do not want it to conflict with other software (Flash) currently working excellently, so my question is will the plug in present problems with other inner works or try to be the default player or what have you? AND if so can it easily be uninstalled again completely? Thank you!
The Unity Web Player is a browser plugin just like Flash. It works independently of Flash and other plugins and you can remove it as you please from your browsers list of installed components.
It in no way tries to be the 'default player'. If the content of the page you are viewing requires the Unity plugin, it will request that plugin, if it is Flash it will request the Flash plugin.
To answer you question, no... It will not present problems with anything, and it will not be the default player, because it only plays games from Unity...
But, just for future reference, the Forums is a better place to post this kind of question...