No, a grandmaster can also consider moves way faster than an amateur. Watch Hikaru Nakamura solve chess puzzles [1]. He has already solved the puzzle and moved on to the next one before an amateur can even see the pieces on the board.

[1] https://youtu.be/4EfSymvT59M

1940s to 1980s papers (the source of the claims) might think "amateur" means something different from people today. (they probably mean club chess players)

Yes? Amateur means someone who does a thing for recreation, as opposed to for money.

It seemed to me that in the chess community, average club players are usually considered (much) stronger than the average online player. (Especially because of the much larger number of lower skill players online.)

So if you measure amateurs via club players (=what people might have considered chess amateurs before), that might give you a different result from the average online player (=what people might consider average amateurs today).

It is much easier to imagine the 1600 FIDE OTB player doing 20-40 positional evaluations than the 1200 random chess.com scrub (eg me) doing the same.

This is mind blowing. He solves these puzzles before I can find the king. How humbling. There probably aren't many instances like this where the gap between world-class and average person becomes this clear.

It's not a tree since you have transpositions. It's a directed graph, since it has cycles.

It does not have infinite cycles because of the 50 move rules and repeated position rules, so the same position is not necessarily the same state/position. Or depending on how you model the data structure, cycles at all.