FM does not transmit to thousands of kilometers...

Only because of the frequencies typically used, not because it's FM

No. The maths show that AM can be received at much lower signal-to-noise ratios.

And FM is intolerant of multipath reception which happens a on SW.

FM is far more restricted by line of sight.

AM is not dead between cities in Texas, if you're into Country, Tejano, or church broadcasts.

The modulation, AM vs FM isn't necessarily the big determine factor on distance. AM can general travel farther on less power, but its more about the frequency choice. FM radio stations usually operate in the VHF/UHF band, which regardless of the modulation technique, it much more likely to be line of site. AM radio stations tend to operate on HF. HF frequencies have a higher change to do bounces. Its more about characteristics of the frequency being used in this case. Under the right conditions, the 6m band, even with FM, can experience "sporadic E" and you can talk quiet far on it.

Yeah but propagation.

The FM receiver that you linked to is actually an AM receiver, but it is using "slope Detection" to recover the audio.

And FM is absolutely not "better" than AM. It does give a clearer signal on strong signals, but is demonstrably worse on weak signals.