Stun, Daze and similar stuff don't impede your movement...
...they make your mind funny.
While you are stunned, there's nothing holding your body to move. You just can't think right to actually do something. If you take a really hard blow to your head, that won't make your body harder to move - it will make your brain go gonzo for a few secs, before you became aware of what's really happening.
Stun is not about movement, is about senses of what's going on.
Freedom of Movement makes "your body work right", not anything else. It allows you to move, but not allows you to think. You can't think if you're dead. Or Stunned.
Paralysis don't block purely mental actions, so it don't block "thinking".
Slow makes your body... well, slower, but it doesn't affect your thinking.
Web is... well, a web. It hinders your body, not your mind.
Stun, Daze, Dazzle and similar stuff, on the other hand, makes your senses go wacko, so they aren't really blocking your movement. Stun never stopped you from moving, it just stopped you from thinking for a while - and since you don't think, you don't act.
So, the point is,
If something affect your senses, Freedom of Movement can't help you.
Think like a "Houdini Effect". Houdini can escape from almost anything, considering that he
knows what's going on. If you throw him with a concussion inside a closed coffin... well... he will stay there.
So, to determine what Freedom of Movement removes or not, use a simple rule:
Why I can't move?
If you can't move because a spell or something is hindering your body to move, like Web, Freedom of Movement can help you.
If you can't move because a spell or something is making your brain go gonzo, like Stun, or because your body becomes something that can't normally move, like stone from Flesh to Stone*, it won't help you.
*Flesh to Stone don't impede your movement, it merely limits you to the movement that a stone statue is allowed to do. A "Freedom of Movement"-ed and "Web"-ed person would become a completely untangled stone statue.
Also, read Freedom, the 9th level spell:
The subject is freed from spells and effects that restrict its movement, including binding, entangle, grappling, imprisonment, maze, paralysis, petrification, pinning, sleep, slow, stunning, temporal stasis, and web. To free a creature from imprisonment or maze, you must know its name and background, and you must cast this spell at the spot where it was entombed or banished into the maze.
Emphasis mine.
Freedom removes a bunch of effects, like Flesh to Stone and Stun. It would seem rather... strange to say that a way lower-level spell can do almost all the things that a 9th level spell can. Freedom is Freedom, not Freedom of Movement.
The creature falls down before becoming prone.
A flying creature cannot be rendered prone. However, the FAQ on flight states:
Flight and Magical Flight: Can a paralyzed or stunned creature keep flying with magical flight? Does a creature with magical flight not apply bonuses or penalties to Fly checks because it doesn’t have a “natural” fly speed? Does flying make a creature immune to being flat-footed?
No, any creature that loses all actions can’t take an action to attempt a Fly check to hover in place and thus automatically falls. That includes a paralyzed, stunned, or dazed creature. Magical flight doesn’t act any differently, even for paralysis, as it isn’t a purely mental action. A creature with 0 Dexterity can’t fly, and paralysis sets a creature’s Dexterity to 0. Despite the fact that the Fly skill mentions that bonuses and penalties from maneuverability apply to creatures with natural fly speeds, they apply for any fly speed. If they didn’t apply to creatures that gained flight artificially or through magic, then those maneuverabilities (like the listed good maneuverability for the fly spell) would have no game effect. Finally, the statement “You are not considered flat-footed while flying” means that flying (unlike balancing using Acrobatics or climbing) doesn’t automatically make you flat-footed or force you to lose your Dexterity bonus to AC; it doesn’t mean that flying makes you immune to being caught flat-footed.
Since the creature cannot take any actions it thus cannot hover and falls down as per the normal falling damage rules. This means that if they hit the ground after falling 10 or more feet, they take the appropriate falling damage and are rendered prone automatically. If they fall less than that, they are rendered prone from the spell.
Best Answer
Hideous Laughter can mostly be summarized as "fall prone & skip your turn"
As you noted, the target can take no actions while laughing.
Moving is an action (PFSRD):
So is standing up (PFSRD):
Taking a 5-foot step ("shifting" in 4e parlance) is an action as well, albeit a weird one (PFSRD):
Attacks of opportunity are not actually actions of any sort (not even immediate actions) as far as I can tell, so the target can take attacks of opportunity by RAW (PFSRD), though this GM would deem that an oversight and disallow AoOs as well.
The part about not being helpless appears to be there to clarify that the target takes no defensive penalties beyond those imposed by being prone (PFSRD):