No, a mug is a (usually china) cup you drink hot drinks from. You don't drink beer from a mug.
Tankards are called tankards in English. This only really applies to the metal beer 'cups', or the really thick glass ones with a pattern of indents and a handle.
The straight sided glass beer 'cups' without a handle are just called pint glasses.
In British English we don't use mug for anything you get beer in. Interestingly, wiki seems to agree with this. I'm not sure whether this means that 'mug' is acceptable in other forms of English and no-one from those countries has bothered to 'wiki' mug, or whether the examples you found are being produced by people with a less than sound grasp of English?
Isn't this interesting. I never thought about it before. I would drink beer from a GLASS mug (which will probably be quite a bit taller than a normal mug), but would find it VERY odd to drink beer from a ceramic mug (like the one in Nona's picture).
But most places around here serve beer in pint glasses or pilsner glasses if it's on tap.