While everything you said is correct, think about the perspective of someone who doesn’t care how it works, only that it does. In this context, ports and recompilation live in the same space as emulation. You and I understand the difference, but we’re nerds. I’m playing the game I bought years (possibly decades) ago, on my pc instead of on a console, with various enhancements depending on what software I’m using and a controller that doesn’t hurt my hands. It’s emulation.
Also, the video I linked probably wasn’t the best choice to make my point, I chose it anyway because it blew my damn mind with how far the community has brought emulation-adjacent gaming.