It's because your CRT is working as it should. Interlacing was invented to provide smooth motion over less bandwidth, and it does exactly that. Its side-effect is a usually undesirable flicker. Interlacing gets a bad rap on HDTV because they are normally designed to broadcast progressively; the thing to take away from this is that it is impossible to display an interlaced broadcast as it was originally designed on a screen that is made to display progressively, hence your CRT that actually can interlace looks nice with your games, and interlaced games look weird or even bad on an hdtv that is always progressive at a fixed resolution.
It might be hard to see or capture, but even on your CRT has another facet that is visible due to interlacing, a zipper-like comb effect along edges of moving objects on the screen. You might need to blink very fast, or use a camera with a fast shutter speed to see it, but it is there, just a lot harder to make out at a fast sync. The old tech was very good at what it was made to do, and that's why it looks so pleasing in motion.