I strongly disagree with the premise that there's a "wrong" way to play retro games. Don't gatekeep. Imagine if people told you not to listen to Pink Floyd unless it's on vinyl. It would be lost media.

That said, CRTs present images fundamentally differently than LCD displays, and a lot of developers took advantage of those idiosyncrasies. There are scanlines everywhere. CRT phosphors aren't square, and appear smaller when darker. Bright pixels can "bleed" into nearby pixels, particularly when using composite signals.

Before LCDs, many (not all) pixel artists used this to their advantage, basically harnessing the imperfections of analog TV to provide equivalents to anti-aliasing, bloom, extra color depth, and even transparency. Some particularly famous examples came from Sega Genesis games. This video goes into good depth on the whys and hows, and there are some solid examples of the outcomes here.

I've attached examples below (hopefully they upload). If you like the raw pixel art, then no harm done. Enjoy! But if you like the way CRTs interpreted and filtered those signals, you owe it to yourself to look up some shaders for your favorite emulator.

(Zero Tolerance, 1994, on the Genesis/Mega Drive)

(Sonic the Hedgehog 2, 1992, on the Genesis/Mega Drive)