That didn't work...
BRILLIANT!!!!????

When you do a Brilliant Move, you usually sacrifice your rook for free!!! How is that Brilliant?? Don't you just give your rook away for free? Take a look!!!
[Event "vs Computer"]
[Site "Chess.com"]
[Date "2023.12.21"]
[Round "?"]
[White "GalaxyGirl253"]
[Black "MittensBot"]
[Result "1-0"]
[ECO "B63"]
[WhiteElo "447"]
[BlackElo "1"]
[TimeControl "0"]
[EndDate "2023.12.21"]
[Termination "GalaxyGirl253 won by checkmate"]
1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 Nc6 6. Bg5 e6 7. Qd2 Be7 8.
O-O-O O-O 9. Nb3 a5 10. a4 h6 11. Bxf6 Bxf6 12. Qxd6 Qb6 13. Qg3 Qb4 14. Bb5 Nd4
15. Rxd4 Bxd4 16. Na2 Bxb2+ 17. Kxb2 Qxe4 18. Nc3 Qb4 19. Rd1 Qe7 20. Qd6 Qxd6
21. Rxd6 e5 22. Nd5 Be6 23. Nc7 Rac8 24. Nxe6 fxe6 25. Bd7 Rc7 26. Bxe6+ Kh7 27.
Rd2 b6 28. f3 Re7 29. Bd5 g5 30. Be4+ Kg7 31. Rd6 Rf6 32. Rd5 g4 33. Nd2 gxf3
34. gxf3 Rc7 35. Kb3 Rc5 36. Rxc5 bxc5 37. Nc4 Ra6 38. Nxe5 Rb6+ 39. Ka3 Rb1 40.
Nc4 Ra1+ 41. Kb3 Rb1+ 42. Kc3 Ra1 43. Bc6 Rd1 44. Nxa5 Rd6 45. Kc4 Rd2 46. Be4
Rd4+ 47. Kb3 Rb4+ 48. Ka3 Rb1 49. Nb3 c4 50. Nd2 Rh1 51. Nxc4 h5 52. a5 Kh6 53.
Kb4 Rxh2 54. a6 Rg2 55. a7 Rg8 56. f4 Rd8 57. Nd6 Kg7 58. c4 Kf6 59. c5 Ke6 60.
Bf5+ Kd5 61. Nc8 Kd4 62. a8=Q Ke3 63. Qe4+ Kf2 64. Nd6 Rg8 65. c6 Rb8+ 66. Kc5
Rf8 67. c7 h4 68. Qd4+ Kg2 69. Be4+ Kf1 70. Qd1+ Kf2 71. Qf3+ Ke1 72. Bd3 Re8
73. Nxe8 Kd2 74. Qe2+ Kc3 75. Qc2# 1-0
It wasn't for free, you got a Knight and Bishop as part of the exchange.

I still have no idea what move we should be looking at. There wasn't a rook sacrifice in the entire game.

15. Rxd4
But Rxd4 is not a rook sacrifice. It's not even an exchange sacrifice, as it wins 2 pieces for the rook.
"Don't you just give your rook away for free?", the OP wrote.

15. Rxd4
But Rxd4 is not a rook sacrifice. It's not even an exchange sacrifice, as it wins 2 pieces for the rook.
"Don't you just give your rook away for free?", the OP wrote.
Agreed.
In terms of material alone, the position is even after the exchange but when we follow it through, the pieces White has remaining can eventually mop up Black's pawns and promote their own which explains why the engine evaluates it so strongly for White and why it's a Brilliant move.

15. Rxd4
But Rxd4 is not a rook sacrifice. It's not even an exchange sacrifice, as it wins 2 pieces for the rook.
"Don't you just give your rook away for free?", the OP wrote.
Agreed.
In terms of material alone, the position is even after the exchange but when we follow it through, the pieces White has remaining can eventually mop up Black's pawns and promote their own which explains why the engine evaluates it so strongly for White and why it's a Brilliant move.
So there are 2 different questions here.
One: Why does the chess.com script call this "brilliant"?
This is clear. It's a sacrifice and it's good. Simple.
Second: Why did the OP wrote "Don't you just give your rook away for free?"
This is a mystery.

I think she was playing against the bot with the help of an engine and hadn't understood that following Bxd4, Na2 wins back the material due to the threat of the fork on the Queen and Bishop. Even then, it's far from obvious why this exchange is so strong for White.

I think she was playing against the bot with the help of an engine and hadn't understood that following Bxd4, Na2 wins back the material due to the threat of the fork on the Queen.
Yes, this is also clear. However, even though she didn't know that then, she must have seen the move Na2 one move later, as this is exactly what happened in the game.

I think she was playing against the bot with the help of an engine and hadn't understood that following Bxd4, Na2 wins back the material due to the threat of the fork on the Queen.
Yes, this is also clear. However, even though she didn't know that then, she must have seen the move Na2 one move later, as this is exactly what happened in the game.
My interpretation is that she did what the engine told her to do by playing Na2 without understanding why it was the best move. Analysing a match like this is challenging for many of us, not least for a 447 rated player.
When you do a Brilliant Move, you usually sacrifice your rook for free!!! How is that Brilliant?? Don't you just give your rook away for free? Take a look!!!
[Event "vs Computer"]
[Site "Chess.com"]
[Date "2023.12.21"]
[Round "?"]
[White "GalaxyGirl253"]
[Black "MittensBot"]
[Result "1-0"]
[ECO "B63"]
[WhiteElo "447"]
[BlackElo "1"]
[TimeControl "0"]
[EndDate "2023.12.21"]
[Termination "GalaxyGirl253 won by checkmate"]
1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 Nc6 6. Bg5 e6 7. Qd2 Be7 8.
O-O-O O-O 9. Nb3 a5 10. a4 h6 11. Bxf6 Bxf6 12. Qxd6 Qb6 13. Qg3 Qb4 14. Bb5 Nd4
15. Rxd4 Bxd4 16. Na2 Bxb2+ 17. Kxb2 Qxe4 18. Nc3 Qb4 19. Rd1 Qe7 20. Qd6 Qxd6
21. Rxd6 e5 22. Nd5 Be6 23. Nc7 Rac8 24. Nxe6 fxe6 25. Bd7 Rc7 26. Bxe6+ Kh7 27.
Rd2 b6 28. f3 Re7 29. Bd5 g5 30. Be4+ Kg7 31. Rd6 Rf6 32. Rd5 g4 33. Nd2 gxf3
34. gxf3 Rc7 35. Kb3 Rc5 36. Rxc5 bxc5 37. Nc4 Ra6 38. Nxe5 Rb6+ 39. Ka3 Rb1 40.
Nc4 Ra1+ 41. Kb3 Rb1+ 42. Kc3 Ra1 43. Bc6 Rd1 44. Nxa5 Rd6 45. Kc4 Rd2 46. Be4
Rd4+ 47. Kb3 Rb4+ 48. Ka3 Rb1 49. Nb3 c4 50. Nd2 Rh1 51. Nxc4 h5 52. a5 Kh6 53.
Kb4 Rxh2 54. a6 Rg2 55. a7 Rg8 56. f4 Rd8 57. Nd6 Kg7 58. c4 Kf6 59. c5 Ke6 60.
Bf5+ Kd5 61. Nc8 Kd4 62. a8=Q Ke3 63. Qe4+ Kf2 64. Nd6 Rg8 65. c6 Rb8+ 66. Kc5
Rf8 67. c7 h4 68. Qd4+ Kg2 69. Be4+ Kf1 70. Qd1+ Kf2 71. Qf3+ Ke1 72. Bd3 Re8
73. Nxe8 Kd2 74. Qe2+ Kc3 75. Qc2# 1-0