#APL(NARS), 69 chars, 138 bytes
APL(NARS), 69 chars, 138 bytes
{w←3 3⍴⍵⋄x←(+/1 1⍉⊖w),(+/1 1⍉w),(+⌿w),+/w⋄3∊x:'win'⋄0∊x:'lose'⋄'cat'}
The input should be one 3x3 matrix or one linear array of 9 element that can be only 1 (for X) and 0 (for O), the result will be "cat" if nobody wins, "lose" if O wins, "win" if X wins. There is no check for one invalid board or input is one array has less than 9 element or more or check each element <2.
As a comment: it would convert the input in a 3x3 matrix, and build one array named "x" where elements are the sum each row column and diagonal.
Some test see example showed from others:
f←{w←3 3⍴⍵⋄x←(+/1 1⍉⊖w),(+/1 1⍉w),(+⌿w),+/w⋄3∊x:'win'⋄0∊x:'lose'⋄'cat'}
f 1 2 3
win
f 0 0 0
lose
f 1 0 1 1 0 1 1 0 1
win
f 0 1 1 1 0 0 1 1 1
win
f 0 0 1 1 0 1 1 1 0
lose
f 1 1 0 0 1 1 1 0 0
cat
f 1 1 0 0 1 0 0 0 1
win
f 1 1 0 1 0 1 0 0 1
lose
