is the hp pavillion a gaming computer if added a better GPU and PSU?

That will depend on the memory as well as board currently installed in that model. Generally the best gaming cases are custom builds where you get to decide just what goes in for everything. This also includes the options for added cooling. Most prebuilds lack the air flow and can lack space if you plan on going with any liqiud cooling setup. The supply and video card look good. The lack of any front or side cooling? doesn't quite make it!
 
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