An instructive ending certainly; it seems that after Luke missed 61 Rg3 it was probably a draw, as GM Ramirez told the commentators, though I haven't checked this with FinalGen yet. The mistakes at moves 57, 58 and 59 had already made it much harder, but Luke was very short of time to reach move 60.
Ian's reasoning was tempting but fallacious as Thomas, hints.
For example, there are two obvious routes to exchange the b-pawns after Black's 61st move.
Either 62 Re5 Bxb3 63 Rb5 Be6 64 Rxb4 or 62 Rd3 Kf5 63 Rd4 Bxb3 64 Rxb4 but the tablebase says both those are drawn.
Likewise, to eliminate the kingside pawns, Luke would only have had to play 62 h4 gxh4+ 63 Kxh4 but that leaves a drawn ending too, as I'm sure he realised.
The position he actually got after 77 Rxb4 would have been a win if it had been his move (or Black to move but White's K on c2). That's how close it was.