Judit Polgar probably good choice. Portisch, maybe not very well known though a top GM. Plus might have to add guys who can seriously play and have chess ideas named after them like Benko and Maroczy.
Best Hungarian Chess Players

You're right Hungary has a large and prestigious chess history. I'll add Leko, Szabo, Adorjan, Lilienthal, Breyer, Sax and Ribli to those already mentioned. Reti maybe qualifies if you like as does Arpad Elo although they were born in the time of Austria-Hungary.

Don't forget Isidor Gunsberg and Johann Löwenthal in the 19th century, Richard Réti and Gyula Breyer of Hypermodern fame, Hollywood Herman Steiner who settled in Los Angeles, or more recently László Szabó, Zoltán Ribli who qualified for the candidates in 1984 and 1986, and lastly András Adorján who gave us the Black is OK series of chess books.
By the way, it was Breyer who controversially said, "After the first move 1.e4, White's game is in the last throes." Ahhhh, leave it to those Hypermoderns. Obviously, Fischer did not agree.

Karjakin now holds the record for youngest age of getting the GM title. Before him the record was held by Carlsen, and before him by Leko.
So records are meant to be broken. I'm not sure it means that much in this information age. Fischer had to do it all without databases or engines, just some Russian magazines in his back pocket.
Just because each was "the youngest grandmaster" doesn't make them World Champion material. In Carlsen's case he's a natural, sort of like Capablanca, and that's different.

My personal choice of GOAT of Hungarian Chess is Lajos Portisch. Imagine being a candidate through interzonal 8 times not including the interzonals in which he narrowly missed the last qualifying spot for the candidates. He was the top board for the Hungarian team that upset Soviet Union in the 1978 Olympiad. He defeated Vasily Smyslov, Mikhail Tal, Tigran Petrosian, Boris Spassky, Anatoly Karpov. He has one of the most number of appearances in Chess Olympiads. He was among the elites from early 60s to late 80s. I am pretty sure many will say Judit Polgar or Peter Leko as their GOAT of Hungary's chess. Its your opinion.

1. Maroczy. 2. Portisch. 3. Leko. 4. Gunsberg. 5. Ribli. 6. Rapport. 7. Szabo. 8. Polgar. 9. Adorjan. 10. Sax
Note that I do not count players like Benko or Lilienthal to be Hungarian since Benko played for the U.S more than Hungary and imo is an American grandmaster and same with Lilienthal for the Soviets.

1. Maroczy. 2. Portisch. 3. Leko. 4. Gunsberg. 5. Ribli. 6. Rapport. 7. Szabo. 8. Polgar. 9. Adorjan. 10. Sax
Note that I do not count players like Benko or Lilienthal to be Hungarian since Benko played for the U.S more than Hungary and imo is an American grandmaster and same with Lilienthal for the Soviets.
It's the same for Isidor Gunsberg (your number 4), who moved to Britain when he was 21 years old.
I would replace him with Charousek and Breyer, who were both world class players in their time, both died young and are mostly forgotten by now.
I'm sure that the top 3 of most people would be Maroczy, Portisch and Leko in some order.
It seems to me that Hungary has produced as many world-class chess players (per capita, at least) over the years as any country out there. So, if a list of the best 10 Hungarian chess players were compiled, who'd be on it?