I think the second “the” can safely be deleted.

<1) The organizers upset the Spanish people by refusing Illescas to play. >

A rare occasion I’d like to add words. Either “refusing to allow Illescas to play” or “refusing Illescas an opportunity to play” would be an improvement.

<got his chance of first class practice.>

Definitely “at” instead of “of”. I’d prefer “competition” to “practice”, but that is less important. So, I’d say “got his chance at first class competition”.

It can be hard to stay consistent in tenses, but I think it’s almost always best to stay in the past tense. This paragraph bounces back and forth some.

<It might be frustrating for Illescas when Korchnoi withdrew>
It might have been.

<and he was still not a welcome substitute, as they would rather proceed with an odd number of players.>

<Illescas, who was unfairly squeezed out in 1989>

I’d prefer “controversially squeezed out” to be more accurate.

<Gelfand was concentrated and did not want to talk with anyone before his game against Kasparov in Round 1.>

I’d prefer “Gelfand was totally focused on his game and did not want to talk with anyone…”

<The best game prize was awarded to Gelfand vs Kasparov, 1990.>

If it’s not known that a prize was awarded, maybe “Gelfand vs. Kasparov 1990 was voted the best game” would be better.

<At the press conference, >

pre-tournament or post-tournament?

<He also revealed that the Kasparov - Karpov World Championship Match (1990) would be held in New York, the first 12 games, and Lyon (France). >

1989: As you say. I wonder about 1) <might have been>, perhaps "must have been" like PMD had it first. And 2) <as they apparently preferred to proceed>, perhaps delete "apparently"? They did prefer that.

1990: As you say, except I now have (if Ok) "Gelfand was totally focused on his first game against Kasparov and did not want to talk with anyone."

<Rentero, nicknamed 'The steam roller' by his fellow citizens, due to his very successful business methods ... >

Following talk of the Spassky contract ...

<All of Kasparov's opponents were literally rewarded for winning or even for not agreeing to a draw before move 40. Such extra prizes usually ranged from £1000-2000.>

Some general commentary:

<The 21 year old Boris Gelfand followed the World Champion closely until the very last round, with Salov, Ivanchuk and Short at times quite close too. All in different styles though. Salov by working immensely hard (his win against Short lasted for a full 162 moves!), Ivanchuk being hard to beat, while Short took a more bumpy road to his points.>

<But of the whole lot, rising star Gelfand was the most impressive. He looked casual at the board, played with ease, preserved his energy cleverly and won game after game at the beginning. Only in his game with Short did things go very, very wrong. Kasparov did as he was expected to, but not as impressively as in Tilburg and Belgrade last year.>

<Kasparov at the final press conference: "Life as a chessplayer is getting tougher".>

- report by IM Bjarke Kristensen.

------------

<GMA Baleares Open> I was in doubt there, but:

1) http://www.bartelski.pl/olimpbase/l... p. 36 cites that name
2) the official logo had exactly that name (I saw a photo somewhere!)
3) https://www.365chess.com/tournament... uses it.

https://zanchess.wordpress.com/2018...

He actually unbound the pages of his volume - which is far and beyond the call of duty. I truly appreciate his efforts - but the main beneficiaries are chess researchers around the world.

I hope this example inspires others.

<Kasparov had fled dramatically from Baku (Azerbaijan) with his relatives only a month before the tournament started.>

The modifier “dramatically” is tough to work in there, but “dramatically fled” would be much better. “fled dramatically” gives a sense of he ran waving his arms wildly, etc.

<The 21 year old Gelfand followed the World Champion closely until the last round, >

“followed” is a bit vague. “trailed” would be a bit better, I think. And maybe “until Kasparov’s win in the final round” would be worth the extra words just to clarify the point.

<with Salov, Ivanchuk and Short at times quite close too. All in different styles though. Salov by working immensely hard (his win against Short lasted for a full 162 moves!), Ivanchuk being hard to beat, while Short took a more bumpy road to his points.>

but the event category would then have gone down to 15.

<The enmity between Korchnoi and Baturinsky comes from afar,>

I would make that "goes back a long way"

<this is a problem between Korchnoi and the organization."">

One quotation mark would probably be enough :)

<also Beliavsky and Yusupov, <who> Karpov may have regarded as 'comrades in arms'.>

I would like 'whom' here

<Gulko apparently wanted to support,>

support him/Korchnoi,

<if there was some mass withdrawal>

prefer 'a' to 'some'

<After leaving Linares, Korchnoi went to the Lugano Open>

<Gelfand, the new star of world chess after his victory in GMA Baleares Open (1989), replaced Manuel Rivas Pastor, who was sick, and Gulko replaced Robert Huebner, who withdrew because he was ill.>

Makes me want to ask for definitions of 'sick' vs 'ill'...

As for the 1990 text I quoted, what I was trying to say was that (without getting into detail on medical conditions) I would go with something like

Perhaps 'Rentero proposed the idea of (having) a separate arbiter...' would be an improvement.

Re <Annie K.>'s idea on the bad blood between Korchnoi and Baturinsky, my thought is that 'The enmity between Korchnoi and Baturinsky is/was of long standing' might well be a better way to set about it.