Analog monitors don't care about the dot clock. They draw lines, but you can put whatever signal you want in the lines so long as the dot clock doesn't exceed the available bandwidth. So horizontal resolution is effectively a range you can change at any time and the monitor won't even notice.

Vertical resolution is very much part of the spec, but even then CRTs will sync to hilariously out-of-spec signals that gain or lose lines per frame. Sanely-designed graphics hardware like the Amiga wouldn't do this, but the Atari 2600 wasn't sanely designed and had plenty of games that played fast and loose with NTSC. Atari graphics hardware only generated a single line of graphics and relied on H-Blank effects for literally everything else. Even the vertical retrace signal was controlled by the game. So it was very common to see badly programmed games send too many lines, and a different wrong number of lines each frame, which nobody noticed until people started writing 2600 emulators.