You are attacking a straw man and the point made is pretty good.
Competition problems are designed to be actually solvable by contestants. In particular, the problems should be solvable using a reasonable collection of techniques and many "prep courses" will teach you many techniques, tools and algorithms and a good starting point is to throw that stuff at any given problem. So just like chess openings putting in lots of leg work will give you some good results for that part. You might very well lose in mid and late game, just like this AI might struggle with "actual problems"
It is of course still very impressive, but that is an important point.
I'm attacking nobody! I literally couldn't understand the point, so I said so: as stated, its premises are simply clearly false!
Your point, however, is certainly a good one: IMO problems are an extremely narrow subset of the space of mathematical problems, which is itself not necessarily even 50% of the space of the work of a mathematician.
Competition problems are designed to be actually solvable by contestants. In particular, the problems should be solvable using a reasonable collection of techniques and many "prep courses" will teach you many techniques, tools and algorithms and a good starting point is to throw that stuff at any given problem. So just like chess openings putting in lots of leg work will give you some good results for that part. You might very well lose in mid and late game, just like this AI might struggle with "actual problems"
It is of course still very impressive, but that is an important point.