We can only argue who gave more of himself to the game.
Who is the greatest chess player of all time ?? Bobby Fischer ??

"It may go a long way in shaping the argument of whether Carlsen has truly surpassed Kaspy."
I don't think so, Kasparov is 53, it's not the same as say a 30 year old Kasparov. Won't tell us that much, but it will say how strong Kasparov still is.
Or reverse the roles, could a 53 year old Carlsen beat a 26 year old Kasparov?:)
The arguments in favor of Kasparov include his longevity as #1 in the world, as world champion, and as a +2800 rated player.
The argument in favor of Carlsen is that he's the current world champion and had the highest rating in history.
If Kasparov can demonstrate that even at 53 he can hold his own against a bunch of next-gen +2800s (in blitz), then it strengthens his case even more.

In my opinion, I would have to say Mikhail Tal... even he intimidated Bobby Fisher with that stare of his. But that's just my opinion. I'm currently reading The Magic Tactics of Mikhail Tal.....it's a masterpiece and I love his aggressive style whether white or black
Keres is in the argument for best player never to be world champion, along with Korchnoi, Bronstein, Nimzo, Rubinstein, and Ivanchuk. Today's young players may still become world champ, so they don't count.
But I don't know of anyone who seriously argues that any of the non-world champions is better than the Olympic Gods of chess history, the actual match-play world champions.
I actually think Topalov is the greatest never to become undisputed champion. Unlike the others, there were periods where he was the best player in the world, he has been ranked no.1 for longer than Anand and Kramnik combined and he lost two very close title matches.
And I agree that the World Champions (barring Euwe) are clearly the best 15 players since the World Championship era began. And I wouldn't put that many players ahead of Euwe either.

Tal lost many games to Keres and Petrosian, during the period he was intimidating guys like Fischer, and to add insult to injury like a patzer.

Tal lost many games to Keres and Petrosian, during the period he was intimidating guys like Fischer, and to add insult to injury like a patzer.
Fischer beat Keres more often than not only won one game v. Petrosian but it was a great one. Petrosian offered a draw Fischer declined and Petrosian made the one error of the game. Also on a side note: why does no one care about poor Gligorich? He played a perfect game with Fischer and draws Fisher most of the time.

Tal lost many games to Keres and Petrosian, during the period he was intimidating guys like Fischer, and to add insult to injury like a patzer.
Tal lost to these guys because the were both positonally defensive which completely dominates his wild attacking style. He beat Fischer because Fischer was more the attacking type. Their styles clashed and their matches were brutal slugfests like Tal liked.
"I agree that the World Champions (barring Euwe) are clearly the best 15 players since the World Championship era began"
I think it is to exaggerate one event though. Let's say Carlsen plays the worst chess of his life in November and would lose to anyone in the top 20. If Karjakin continues to stay around #10 in the world and never gets close to be top three in the future either, would he still be "better" than for example Korchnoi, who was #2 for a decade behind only one of the greatest greats? Maybe overly hypothetical example, but I think the result of one event is less important than the career achivements on the whole.

I think that Jan Timman is very much underestimated. Is/was a good player. But my favourite is Kasparov.

Tal lost many games to Keres and Petrosian, during the period he was intimidating guys like Fischer, and to add insult to injury like a patzer.
Tal beat a 15 yo Fischer 4-0 in one event and never managed to beat him again ... big deal .

Chess fail, that would probably be, in order,
Philidor
Lasker
Steinitz
Kasparov
Morphy.
That doesn't mean they are the best of all time. Pretty much every chess historian accepts that chess is progressive. Today's players have learned from the past.
Morphy was better than Philidor, Steinitz surpassed Morphy, and so on.
Kasparov is playing an important blitz tnmt this week. It may go a long way in shaping the argument of whether Carlsen has truly surpassed Kaspy. If Kaspy breaks even with these guys, he will show that his best is still arguably the best ever.
I'm not so sure it proves much . Nakamura is the strongest blitz player of the 3 I believe but Caruana is known to be weaker in blitz than most 2750+ players and I dont know how good So is in blitz . Would be better test for Kaspy if the 3 he were facing were Carlsen , Grischuk and Karjakin ? At age 53 surely he will have slowed some in blitz and this will hurt more than a slight decline in his ability imo .
"I agree that the World Champions (barring Euwe) are clearly the best 15 players since the World Championship era began"
I think it is to exaggerate one event though. Let's say Carlsen plays the worst chess of his life in November and would lose to anyone in the top 20. If Karjakin continues to stay around #10 in the world and never gets close to be top three in the future either, would he still be "better" than for example Korchnoi, who was #2 for a decade behind only one of the greatest greats? Maybe overly hypothetical example, but I think the result of one event is less important than the career achivements on the whole.
Sure thing, hence why I excluded Euwe but all 15 of the other World Champions have such numerous accomplishments in addition to their title.
"all 15 of the other World Champions have such numerous accomplishments in addition to their title"
They do have that, but on some occasions it has been really close that "below Korchnoi" level players won the title, as when for example Leko and Schlechter drew title matches without maybe ever being among the three best players in the world at any point of their careers. Also Bronstein would find it hard to compete with Korchnoi even though he drew a title match, and Gelfand drew one against Anand before the rapid tiebreak. I think that, as soon as Carlsen loses interest, it soon will be time for another World Champion that will not be Keres or Korchnoi level. It's just so even behind Carlsen that no one is clearly better than anyone else in the top ten.
Karpov's live chess rating did indeed surpass Fischer's all-time best, but not by a statistically significant amount.
The chess world was robbed of a great series of world championship matches when Fischer declined to play Karpov.