"Skype" is just a brand in English- although some people use it as a verb, it it not widely used in this manner, so translating this as "I Skype with Mark" is really less appropriate than the literal translation....
It's widely used as a verb where I am (native American English speaker). I would find it awkward to communicate this sentence without using Skype as a verb, actually.
Well, since English->Ukrainian course is the only way to learn this language with DuoLingo, many non-native english speakers (including myself) use it as they have no other option. It took me a while to recognise "skype" as verb.