If you have watched this scene from the Queen’s Gambit Luchenko is in a losing position. Based on Beth's experience Luchenko has lost.
In a fan fic Queen Elsa vs. Beth Harmon | Episode 8 | The Lost Episode of Hope on YouTube, Elsa still gets out of Beth's traps.
Nice game of Beth Vs. Luchenko. Beth played very well and Anya has done some great acting. Luchenko did the gentleman thing here to resign. As a twist of plot, here is an alternate idea. Qe4!!!
Luchenko: "Oh no! My queen is under attack, the king and rooks are pinned!"
Beth: "I've got you cornered."
Luchenko: "It's time to drink some Rick-rolling juice!" **Music Starts**
Beth: "Who is Rick?"
Luchenko doesn’t need to resign so soon as white on Qe3. He can simply move white to Qe4 which protects the f3 checkmate from Beth. F3 is the weak square here for Luchenko.
Here are some possible game continuations out of hundreds of billions of games out there:
1. Qe4 Bxg1, Kxg1 Rxe1+, Qxe1 Qxf3, Qe7+...
(Beth cannot do Kg8, Be6+ Kh8, g7+ g8=Q+, Kh6 Qeg7# = Mate in 4)
If Kh8, Qe8+ Kg7 (forced move for Beth to escape Mate in 1)
Luchenko can repeatedly go to Qe7+ Kh8, Qe8+ Kg7, Qe7+ Kh8, Qe8 Kg7, Qe7+ Kh8... in a perpetual check since Beth won't give up her black queen to the squares Qf7 or Qf8 or else it's a guaranteed mate in 1-6 from Luchenko. (Luchenko can go for a queen or knight promotion and deliver mate in 2 gxf7 Kg6, f8=N+ Qf6# or Kh8 f8=Q# in these sample hypothetical scenarios which Beth doesn't fall for.)
"Oh no, it's a DRAW!"
If Kh6, Qh7+ Kg5 (forced), g7 Rxh7 (forced, if Rh1+ Beth loses), and Luchenko goes g8=Q+ for a check.
If Qd1+, Kf2 Rxh7 is alive again and Luchenko goes g8=Q+ for a check.
"Luchenko is back in the game alive at 50/50 odds with Beth!"
2. Qe4 Re5, Qxe5+ Bxe5, Rxd1 Qxf3+, Ke1 Qe3+,...
3. Qe4 Bxg1, Rxd1 Re5, Qg4...
(The tables have turned Miss Harmon? As a Grandmaster, Beth probably wouldn't get into this blunderous ending.)
4. Qe4 Rxe1, Kxe1 (unpinning the king) Bxg1 (free piece capture from Beth)...
Am I missing something here?