I know im 2 years late but I think its really a tower but a 'siege tower'(a tower that has wheels)
Does Anyone Know What A Rook Is In Real Life?

In my opinion, after read all of your comment, it kinda make sense to me. It can be bird or tower.
If it bird, thats mean it's trained bird that can bring important message (messenger birds). It also can be mean as a spy or informan, or assasin.
If it tower, it can be also wall/gates, or watch tower, that can see the enemy from a far within a certain area. I mean try to imagine, if you are a soldiler that guard the wall castle, but you are placed on guard over the castle walls and your main weapon is a long-range weapon like a bow arrow or cannon or artillery. When you are placed there you can see far ahead in a certain distance, you can even use binocular to see more far. I mean you can see anything coming through the castle gates, if it enemy that come to harm, you can easly kill it with your long range weapon.
This explain why it can move as many squares as it likes left or right horizontally, or vertically. And it's also explain it place in the corner which mean far from king and queen. And if you wonder why the tower can move, just imagine it not wall that move but imagine the one that move is weapon (long range weapon) like artillery.
and zoomerboom