In "One Night in Bangkok." Freddie says "Thank God I'm only watching the game, controlling it." This ties in with his subsequent appearance as a media personality. He gives a little bit of narration for the cameras; we have the reversal where in Act I, Freddie antagonized the media, and in Act II he is one of them. This is definitely intentional, although it's not pulled off to its fullest effect.
After this, "The Interview" features Freddie basically attacking Anatoly on the air. He also takes multiple swipes at Florence. This is believable; Freddie is bitter about losing the title, and about what he sees as Florence's betrayal, and has just been unexpectedly given the green light by Walter to take all that out on them. So far, we have a consistent arc from Freddie.
That arc is abruptly cut off in "The Deal." Literally in the scene before this, Freddie was humiliating Anatoly on live television (to the point where Anatoly runs out of the studio before the interview ends), and now he's reaching out to him on Florence's behalf. At this point Freddie is literally the worst person on the face of the earth to send to convince Anatoly to throw the match. Anatoly is completely justified in blowing him off.
Then Freddie approaches Florence, in a "desperate final play." I've already talked about this at some length, and here I just want to point out that a few days earlier he was taking cheap shots at the woman he now claims to still love. This is a dramatic shift in character with no build-up, but it can work - Freddie has a sudden realization when he sees Florence that he still cares about her. It's the kind of thing that a musical can pull off, once.
But to try it twice in the same act is going too far. And in "Talking Chess," out of nowhere, Freddie wants to help Anatoly because he can't stand to see a "mediocrity" like Viigand win. So he tells Anatoly that Viigand's King's Indian Defence has a flaw in it.
This is one of the few times we actually hear the characters talk about chess. The King's Indian Defence was not the Sicilian in terms of popularity, but it was still a very well-explored defence in terms of top-level play in the late 20th century. So it was a well-chosen defence, at least.
But Freddie at first wants to humiliate Anatoly, then he's in love with Florence and wants her to come back to him and "bring back the golden era." Okay, we can live with that. But now he really loves the game of chess? And not only loves it, but he loves it enough to rescue Anatoly's match, giving him information that presumably will help Anatoly to win, which in turn will cost Florence a chance to see her father. You know, the woman he just declared that he still loves?
The idea of loving chess itself isn't a bad one; in a number of productions, actually being chess players seems like a formality that the characters are going through in order to focus on international intrigue, fame and affairs of the heart. We know from "Pity" that chess was Freddie's respite from a bad home life as a child. But really, this isn't about his feelings about chess. It's about how he feels about Anatoly.
You see, if the conclusion is that letting Viigand beat Anatoly is letting mediocrity win, then the necessary premise is that Anatoly is great. Freddie has come around to thinking that Anatoly - who pretty much beat him primarily because Freddie was playing awful chess under emotional duress - is so much greater of a player that he deserves to represent chess as its world champion.
To be honest, I don't buy it for a second. I understand the idea that Freddie really loves chess as a game, but not that he's suddenly gained a respect for Anatoly that he clearly never evinced anywhere else in the show. There's not even a hint of grudging respect; "He's the best Red on the circuit" is a textbook example of damning with faint praise.
After "Talking Chess," Freddie delivers a snippet of media introduction to the Anatoly/Viigand finale, and then disappears from the show. Since that is pretty much meaningless from a character standpoint, it means that this is the end of his very strange character arc. He doesn't even merit a further mention. It's a totally unsatisfying way to conclude for a character who dominates the opening of the show as totally as Freddie does.
"Talking Chess" is meant as something of a redemption moment for Freddie, but it doesn't work, because he's bounced around so much. Helping Anatoly beat Viigand is not the redemption the audience wants to see for Freddie. This is part of the split-match motivation problem; there's too much truth to the line "How many times do you want to be champion anyway?" from "The Deal." The audience wants Florence to get her father back, and in that context helping Anatoly win is not going to make Freddie seem like less of a jerk.
It's somewhat apropos that Freddie goes out on a bit of narration in Act II of London Chess. He bounces around so much in the act in terms of motivation that he's left effectively as a plot tool and little more. And until the 2008 concert, he doesn't even get "Pity" in this act.