I rewrote this to:

if ( $x = !!$y || 0 ) {
 ...
}
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I'm sorry, but that's just awful. I'd never guess what you were actually trying to do here if I stumbled across this code, regardless of how correct it might be.

In my opinion there's not much wrong with your first example, and although the conditional operator does add some brevity, the if else construct is almost certainly more readable to more people.