The order of strokes affects the "evolution" of the character when writing in high speed. In high speed the character shape shifts and one can often recognize the character even after extreme deformation because the general flow of the character is there. But if the stroke orders are changed, the deformation doesn't conform to the expected shape and it may be unrecognizable to other people.
For example, imagine the "s" in the word "best". If written in high speed the end of the "e" touches the top of the "s" and the "s" deforms to look like a "backwards C". Imagine if people wrote "s" with the "e" touching the bottom of the "s". i.e., the "s" is written from bottom-up. Now under high speed, the "s" actually looks like a well formed "s" but the "e" and "t" are deformed, make the word "best" look weird.
High speed writers can make characters look almost nothing like it's proper counterpart, but people have learned to recognize them and recognize other people's handwriting because the stroke order affects the form.
Also, following stroke order helps computers recognize characters better. Under high speed, a character will look totally different from it's proper form, but a trained computer can recognize the direction and order of the strokes and can recognize the character based off of that alone, rather than trying to recognizing the end image. I would imagine that that results in fewer false positives than recognizing by image alone.