@Linkat,
Well done for all your busy googling! It's so much better than constructing your own sentences. Just because you can find something on the internet doesn't make it true. It reads like a first year student's essay, I wouldn't give it much creedance, unless of course it's aimed at someone with a rather rudimentary knowledge of literature. They did get one thing right though,
It needs to be expressed - you can use "tone" in language.
Otherwise, it's irony, or satire. I agree with you that some of Shakespeare's characters could be sarcastic. What leaps to mind is Mark Antony's speech following the assassination of Caesar.
'(For Brutus is an honourable man,
So are they all, honourable men)'
Overall though I would say that irony is a far greater feature in Shakespeare's play, Falstaff's 'Discretion is the better part of valour,' springs to mind. There's no sarcasm there, or the drunken porter scene in Macbeth following the murder of Duncan. Overall though I would opt for the character of Malvolio as being the most ironic, particularly where he is shut up in the dungeon pleading with the 'priest' who is in reality the Jester Feste.
I really think your source is aimed at someone who really doesn't understand irony, and needs to be guided towards the meaning by comparing it with sarcasm, a concept that is much easier to grasp.
I do welcome the opportunity to discuss Shakespeare, as it doesn't happen that often. So who would you say is the most sarcastic character in Shakespeare's plays, and who is the most ironic?