It's not gaming the system if you meet the requirements to collect unemployment by your states rules.
You may think you don't need the money, morally are not entitled to it, or shouldn't take it because you were going to retire anyway. However, we don't know what will happen down the road. Maybe things don't work out the way you intended and you really do need the money down the road. Well, at that point you can't turn time back and collect what you were once entitled to.
Unemployment rules in many states have been relaxed and expanded due to the pandemic. As an employee, you have been paying in to your states unemployment fund for as long as you've been working. Further, the additional amount being kicked in by the federal government is a cost being borne by all taxpayers, you included.
Bottom line, apply for it, and accept what you are legally entitled to. There's no shame or anything to feel ashamed about, it's simply a step in the system which you have been participating in and are entitled to claim benefits from at this time. Have you been receiving the stimulus payments thus far? It's no different in my mind. Most folks on this site really do/did not "need" them. Did anyone refuse to accept theirs? Highly doubtful.