After 52. Kd2 the White King has no legal moves. The move 52...g3? does not give a check and results in a stalemate since the White King may not move into check. A stalemate results in a draw; IM Daniel Rensch explains it on video in What is Stalemate in Chess?.
Both (52...Re2#) andBlack has a variety of moves (52...Qc1#6) getto finish the job done.:
- (52...Re2#)
- (52...Qb4#)
- (52...Qc1#)
- (52...Qc2#)
- (52...Qd3#)
- (52...Qd4#)
[Title "From White's Perspective"]
[FEN "8/8/4k3/4rb2/2q3p1/8/3K4/7r b - - 0 1"]
[StartFlipped "0"]
1... Re2# (1... Qb4#)(1...Qc1#)(1...Qc2#)(1...Qd3#)(1...Qd4#)
Related:
Why was this a draw?
Why is this position stalemate?
Why was this stalemate?
Why is stalemate a draw?