In 1915, he won the Mechanics' Institute chess championship. In 1921-22, he won the first California State Championship with a perfect 10-0 score. He also won the California Championship in 1922, 1926, and 1927. That’s all I could find.
For winning the 1920-21 which was held at the Mechanics’ Institute in San Frncisco from December 27, 1920 to January 8, 1921, Gruer received $100 (about $1,655 today), a gold medal and a rotating trophy. 
[Event "1921-22 California Chp, San Francisco"]
[Site "San Francisco, CA USA"]
[Date "1922.01.05"]
[Round "?"]
[White "Elmer W. Gruer"]
[Black "S Swanson"]
[Result "1-0"]
[ECO "D11"]
[Annotator "Stockfish 16"]
[PlyCount "61"]
[EventDate "1922.??.??"]
{D11: Slav Defense} 1. d4 d5 2. Nf3 c6 3. c4 dxc4 4. e3 b5 5. a4 Bb7 6. Nc3 {
Almost always seen here is 5.a3, but there is nothing wrong with the text.} a6
7. Ne5 {This is premature and results in black getting a slightly better game.
White's best play was to challenge on the Q-side with 7.b3 or 7.axb5 with full
equality in either case.} Nd7 8. Nxd7 Qxd7 9. b3 cxb3 (9... e5 {is more
aggressive, but also more complicated!} 10. axb5 (10. dxe5 Qxd1+ 11. Kxd1 cxb3
{is good for black.}) 10... Bb4 11. Bb2 cxb5 12. bxc4 exd4 13. Qxd4 Qxd4 14.
exd4 Nf6 15. cxb5 Ne4 (15... axb5 16. Bxb5+ Ke7 17. O-O {White's extra P will
not amount to much.}) 16. bxa6 Bd5 17. Bb5+ Kd8 {Other K moves lose!} (17...
Ke7 18. Ba3 Bxa3 19. Nxd5+ Kd6 20. f3 Bb2 21. Rb1 Nc3 22. Nxc3 Bxc3+ 23. Ke2 {
and white should win.}) 18. Rc1 (18. O-O Nxc3 19. Bxc3 Bxc3 {Black is clearly
better.}) 18... Rc8 19. Ke2 Bxc3 20. Ba3 Rb8 {Black is a piece up.}) 10. Qxb3
e6 11. axb5 axb5 12. Rxa8+ Bxa8 13. Be2 Bd6 14. Ne4 {[%mdl 1024]} Ne7 15. O-O
O-O 16. Bb2 Bb7 17. Bf3 Bb8 18. Nc5 Qc7 19. g3 Ba8 20. Ra1 Ba7 21. Ba3 {
[%mdl 32] So far the game has been pretty boring what with all the shifting of
pieces. Even black's Bs huddled in the corner do not confer any advantage on
white. However, black is facing a hidden danger which he could have eliminated
by playing 21...Bxc5 which results in equality.} Re8 {The losing move.} 22.
Nxe6 fxe6 {This only cooperates with white and speeds up the winning process.}
(22... Qb7 23. Bc5 Bxc5 24. Nxc5 Qc7 25. Qa3 {It might be hard to see, but
white has a decisive advantage!. For the record, Stockfish finally delivered
mate on move 93, so clearly this is the line black should have chosen!}) 23.
Qxe6+ Kf8 24. Bd6 Qb7 25. Bh5 {[%mdl 32]} g6 26. Bg4 {White wants to mate with
Qf6+.} Kg7 {Prevents Qf6+, but white still has a mate.} 27. Be5+ Kh6 28. Bf4+ (
28. Qf6 {mates at once i.e. 29.Qh4#}) 28... Kg7 29. Qe5+ Kf7 30. Be6+ Kf8 31.
Bh6# {A very nice finish!} 1-0
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