This is definitely my last one in the series; getting too hard to avoid words already used in prior ones. Also forgive me for the slightly off-chess reference in 21 across - its my favourite book. Enjoy.
Chessword 5

8 Across:Steinitz
14 Across: Aronian
39 Across: Caissa
3 Down: Triangulation
5 Down:Fine
27 down: Engines

3 down: Triangulate
2 down: opposition
4 down: euwe
13 down: check
31 down: spite
35 down: sac
38 down: pin

Anyone have a clue about 17, 22, 25 down? It was the one bit I was rather pleased with this time around.

21 Across: Azad
16 Across: Mednis
24 Across: Blitz
10 Down: Kingside
30 Across: Zugzwang
29 Across: Positional ?
For 17, 22, 25 down, I think
17 Down: Judit
22 Down: Zsuzsa
25 Down: Zsofia
which would make
36 Across: Polgar
21 Across: sisters

Excellent except you got Zsuzsa and Zsofia the wrong way round. The Z in zugzwang connects with Zsuzsa's centre.

2 Down: Outside Passed Pawn
12 Down: Grade
15 & 41 Across: Zonal Tournament
15 Down: Transpositions
18 Across: Havana Chess Club
19 Down: Hush
20 Down: Standalone
23 Across: Sisters
28 Down: Strong
32 Across: Without Compensation
32 Down: Torre
37 Across: Eatin' Pieces ??
40 Across: Edge

Chessword 5 Solution
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Well done, guys. Definitely my last crossword - I am sick of them. Attempting something different at moment.
Chessword 5
1
2
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5
6
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17
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32
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34
35
36
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40
41
Across [1] Player once banned by Manhattan Chess Club for his clothes (6,5,7) [8] First undisputed world champ (8) [9] Combinations sometimes called see-saws. (9) [11] Very fast time control (9) [14] Armenian national hero (7) [15] See 41 across [16] First player to beat Fischer in US championship (6) [18] Venue that lays valid claim to Capablanca (6,5,4) [21] Fictional boardgame from book The Player of Games by Iain Banks (4) [23] See 36 across [24] Quick game (5) [26] Leave a piece unprotected (4) [29] Subtle manoeuvring (10) [30] Everything loses (8) [32] Nothing to show for the material (7, 12) [36 and 23] Talented trio (6,7) [37] Usually leads to a win (5,6) [39] Chess goddess (6) [40] Slight advantage (4) [41 and 15] First qualifying cycle of world championship (5,10)
Down [2] A major advantage in endgame (7,6,4) [3] Trick to gain opposition in endgame (11) [4] Fifth world champion (4) [5] Reuben, great US player (4) [6] File with a pawn missing (4,4) [7] Also known as the Petrov defence (7) [10] Where most attacks happen (8) [12] An attempt to put a value on your ability (5) [13] Attempt to maintain the initiative (5) [15] Ways to meander back on to the path (14) [17] One of 36 across (5) [19] Frequent demand of arbiters (4) [20] Type of chess program or machine (10) [22] One of 36 across (6) [25] One of 36 across (6) [27] Rykba and Houdini (7) [28] Describes a good player or move (6) [31] Check given just to delay the end (5) [33] Attack characterised by Bg5 (5) [34] Postal governing body (1,1,1,1) [35] Calculated offering (3) [38] Restricting tactic (3).