I completely agree with the above answers.
Thought I would share some furthers insights
A command is the most forceful way to tell someone to do something.
Commands are more powerful the shorter they are.
When you are training a dog, and trying to assert your power you tell him to "sit" /"stay"
'click this link' is more slightly more powerful than 'click on this link'
(even though not much)
Often we see 'click this link' in the context of advertising.
Marketing relies on creating a powerful message. If omitting the on helps even a little, then this is what they will do. In turn this is what we become accustomed to seeing, and therefore continue to use it.
As another point:
You cannot say click on your fingers... but rather click your fingers
(the same way as you wouldn't say -'bend on your arm)
Maybe click (without on) is used commonly with regards to computers as a way of differentiating.