I don't think the argument presented there works.

Consider the example with A, B, and C at the end. It claims that approval voting would probably elect C, but why? If the voters apply perfect strategy, B supporters won't approve C, and B will win. The same is true of range voting, where B supporters will give C a rating of zero.

It does not seem escapable that a majority voter block can dictate their wishes on the whole population by exaggerating their stated preferences.

As long as you need a majority, that's still very democratic? (If it was a plurality only, that would be harder.)

Yes, but the page in question is arguing that approval/rank voting is better because it doesn't always elect the majority's first choice.

I'm pretty convinced that for single winner elections approval voting is pretty great.

I haven't convinced myself when multiple people can get elected.