I vote for someone having an affinity for bad coding style. That's the only explanation I can see for both the for loop and the i++ being placed inside of an array subscript. I think this would be better:

while (i < length && callback.apply(object[i], args)) { i++; }

Or if you happen to feel that the === operator in the original example has value, then:

while (i < length && callback.apply(object[i], args) !== false) { i++; }

Another possible reason for doing this may have been as a performance optimization. Although this quick benchmark that I put together seems to disprove that theory. On Windows the while loop above is 20% faster than the original for loop in Chrome, in IE and Firefox both loops perform the same. On OS X the for loop has a 10% advantage in Firefox, there is no difference between the two in Chrome, and Safari prefers the while loop by 6%.

So from a performance standpoint it's a wash. If anything then judging by market share you would probably want to optimize for Chrome on Windows before optimizing for Firefox on Mac, in which case the while loop would be preferred.

Which says to me that it's unlikely that performance optimization played a factor with this code. And I return to my original theory that it's just an example of poor coding style making it past the code-review process.