If I read this correctly and my understanding of JavaScript precedence is correct, I think this is an ugly version of a big else-if statement. Something like this:

if (aw == null) {
return a0 === "!=";
} else if (a0 === "=") {
return a2 === aX;
} else if (a0 === "*=") {
return a2.indexOf(aX) >= 0;
} else if (a0 === "~=") {
return (" " + a2 + " ").indexOf(aX) >= 0;
} else if (!aX) {
return a2 && aW !== false;
} else if (a0 === "!=") {
return a2 !== aX;
} else if (a0 === "^=") {
return a2.indexOf(aX) === 0;
} else if (a0 === "$=") {
return a2.substr(a2.length - aX.length) === aX;
} else if (a0 === "|=") {
return a2 === aX || a2.substr(0, aX.length + 1) === aX + "-";
}

return false;

which you could also write as

return (aW == null) ? a0 === "!="
: (a0 === "=") ? a2 === aX
: (a0 === "*=") ? a2.indexOf(aX) >= 0
: (a0 === "~=") ? (" " + a2 + " ").indexOf(aX) >= 0
: (!aX) ? a2 && aW !== false
: (a0 === "!=") ? a2 !== aX
: (a0 === "^=") ? a2.indexOf(aX) === 0
: (a0 === "$=") ? a2.substr(a2.length - aX.length) === aX
: (a0 === "|=") ? a2 === aX || a2.substr(0, aX.length + 1) === aX + "-"
: false;

where this shows the IF on the left and the RETURN THIS on the left of the "?" on each line. Ugly. Un-maintainable. Yuck.