Battleship

Also, the way the pirate is using it in her video, you wouldn't be dismounted very often anyways. O_o

...

Since I still don't know why Nexon put it in this way, does the durability decrease with time? Since it is compared to a mount, I can compare it to tiredness?

Perhaps, but you'll notice she uses Ice Splitter a lot to avoid being attacked on two sides at once, a tactic that doesn't work at bosses.

And as for the second question I've quoted, while it doesn't work entirely like that, take a look at the top-right corner when she turns on battleship - the darkened part of the buff which normally indicateds time spent is already almost full. Again, it's pretty much known by now that it's the battleship's HP, and you can see that even with the repeated mount/dismounts its HP doesn't go back up.

So, I suppose you could refer to durability like tiredness that only goes up when you get hit and down after the 'break'. (Though I'm not sure how re-logging would affect the skill)