One more from the Collins Cobuild English Dictionary
If you click on an area of a computer screen, you point the cursor at that area and press one of the buttons on the mouse in order to make something happen.
I clicked on a link and recent reviews of the production came up.
Click the link and see what happens.
From those dictionaries, the usage seems to be unpredictable!
"click on a link" and "click the link" both exist in Collins Cobuild Dictionary.
"click on" is repeatedly introduced in Longman series.
"double-click on the icon" and "click the left mouse button" are found in Oxford system.
It seems like a writer's option?
This is what I found in the dictionary.
Longman Activator Thesaurus
click on /ˈklɪk ɒn/ [transitive phrasal verb]
to press a button on a mouse in order to choose something on the screen and make the computer perform a particular action:
Click on ‘next’ when you have finished filling out the form.
Longman Phrasal Verbs Dictionary
click on sth
to make a computer perform an operation by pressing a button on the mouse in order to choose something on the screen. A mouse is a small object connected to a computer, which you move with your hand to give commands to the computer
Once you have entered your data, click on OK.
Click on the printer icon with the right mouse button.
Longman Dictionary of Contemporary English
2 [intransitive and transitive] to press a button on a computer mouse to choose something from the screen that you want the computer to do, or to press a button on a remote control :
Choose the image you want by clicking twice.
Children can click on a sentence to hear it read aloud.
Oxford Advanced Learner's Dictionary
2 ~ (on sth) to choose a particular function or item on a computer screen, etc., by pressing one of the buttons on a mouse
Click the OK button to start.
I clicked on the link to the next page of the website.
To run a window, just double-click on the icon.
Oxford Dictionary of English 2nd Edition
■ Computing press one of the buttons on a mouse to select a function or item on the screen: [no obj.] you can click on an underlined word to jump to another section | [with obj.] click the left mouse button twice.