Don't get confused with Precedence and Order of evaluation.
The order of evaluation of logical OR || is left to right.
So if left = true then left || right will never execute right. In your code exactly same happened.
As you know, any non zero value treated as true in C, hence, ++i or -2 is true. So,
m = ++i || ++j && ++k;
m = true || bla bla bla; //right not even checked!
m = true
m = 1
And you get the output as expected.