Would I have to pay Royalty on video rendered out in Unreal Engine 4, used in a separate game engine?

I don’t know what you mean by JR citations.

Based on your comments, it sounds like you don’t disagree that the resulting game would be a Product under the EULA. If you’re not following that line, I can walk you through how that works in the EULA.

It sounds instead like you’re saying you don’t think the EULA, or at least part of it, would be enforceable in court. I certainly disagree, but I don’t think this is the appropriate venue for discussing litigation strategy.