clip 1: https://youtu.be/tcs1WNZUnlE

First of all, as seen from the video, Mars' arena does not block flying units from simply flying in and out. This also means flying units cannot be speared into the wall (but can still be speared to trees, buildings and cliffsides for some reason?)

Here are some explanations from the video

1. Clockwerk's jetpack gives flying movement, so he can freely fly in and out.
2. Batrider's Firefly has been changed to no longer give flying vision (and inadvertently flying movement**) since 7.23. However, since Valve coded this by removing his flying movement and giving batrider free pathing instead, this meant that firefly is not flying movement (despite its alt description), and thus cannot escape Mars' arena.
3. Dragon Knight's aghs just gives him free pathing but not flying movement. This is why he can "fly" over terrain but not over Mars' arena.
4. Night Staker gains flying movement during ulti, so he can freely fly in and out.
5. Winter wyvern gains flying movement during her Arctic burn. Which gives her the ability to fly in and out.

Note that Arctic Burn also no longer provides flying vision since 6.78 just like batrider, but WW still gets flying movement. This is different from when Batrider lost his flying vision in 7.23 but also lost his flying movement. Why was both skills coded differently? I have no idea.

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clip 2: What cannot escape vertically means

Secondly, this is what Valve meant by fixed vertical skills from escaping arena. Skills that used to be able to "jump" out over the area no longer does since the knockback has higher z-axis effect.

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Solutions/ How to make it more clear:

1. Add a mention to Mars' Arena that it does not affect units with flying movement
2. Fix batrider either by giving him flying movement, or removing "fly" from his skill description

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Bonus section: How to defy Valve's spaghetti coding and escape Mars' Arena with vertical (z-axis) movement skills.

clip 3: How to bypass spaghetti code and escape Mars' arena

During my testing, I found out that valve coded Arena to prevent vertical (z-axis) escaping by having the undead warrior attacks have a higher z-axis hitbox so it can knock you back inside if you try to jump over. But since knockback can only occur every 1 second, you can intentionally bump into the wall to get knocked back and immediately jump out to escape.

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TL;DR

Either arena is working as intended and the only bug here is Batrider's firefly not give flying movement as described in his skill (It only gives free pathing).

OR

Valve made a mistake since Mars' launch and forgot to code Arena to affect flying units.

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Bonus clip: Walrus kick ignores Arena's knockback for some reason.