Shell script to count chess game outcomes
I don't see the reason for chaining with -print0 | xargs -0. 
It's better and simpler to use -exec:

find . -type f -name '*.pgn' -exec mawk -F '[-"]' '...' {} +


I don't see a way to make the AWK code faster, 
but:


Some of the double-quoting is unnecessary
I would add a space around operators for somewhat better readability
A semicolon can be dropped


Like this:

/Result/ { ++a[$2] }
   END { print a[1] + a[0] + a["1/2"], a[1], a[0], a["1/2"] }