...or did everyone just rush past and capture the empty Castle?

Exactly. There's no need to fight the opponent – the goal is to win the scenario, where the victory condition is capturing a Castle...

As it turns out, you can capture it on the tenth day, although capturing a Castle is a technical matter. The task of the map was to reach the Castle as quickly as possible, having an army large enough to clear the obstacles in the way... The tactic is very simple. The shortest route is over water. Personally, I managed to land on the enemy's shore at the end of the ninth day – and I was only two steps away from capturing the empty Castle on the following tenth day... I tried everything, but it didn't work out. :(
I had to take two days to slowly approach, so that the dumb AI would make a gift and leave the Castle...

That's why it's interesting to see the description of the playthrough of the top five players – they have very similar results...

Added 6 minutes later

I sent the description to Ataman, so if anything, he can post it.

They came up with a practice of passing the description to the discretion of the host... :) He only needs it to credit your save and that's it. And for those who want to see your result, you can post the description yourself right here...