"What proportion of games do actually end that way."
To date 6902 championship have finished. Just 220 Rd1 games to go! (7122-6902).
So far 6 have ended in stalemate.
So the average is approx 1 stalemate every 1,150 games.
The game in question has finished. Game 9099814
It was obvious the lad was going for a stalemate from move 26
when he gives up his Rook and Bishop.
I can understand the frustration but you are a sub so you can
have as many games as you like. Non subs I think feel this more
especially if they are involved on one of these 21 days a move games.
In the actual game 17.Qe6+ instead of 17.b4 batters him off the board.
Also after you queened I looked for a quicker win and there is one.
Instead of 36.Qe8+ the move 36.Qb5 cutting off the flight squares
was quicker. Black can do nothing to prevent to 37.Rd4 mate.
(In these situations cover the flight squares, then any check wins.)