The word is also used in Urdu/Hindi..Shareek...it comes from the word Shirk, to place two things together, to put two at a par, etc.
Theologically, shirk has different categories. Akbar, ASghar, Jahri, Khafi.. Theologically speaking, Shirk Akbar can take one outside the established bounds of Islam.
Shirk Khafi (hidden) is like someone praying beautifully to show off to others, giving charity with the intent to be praised as as Dayavaan. Such shirk is reprehensible, but doesn not make one a non muslim, though it does spoil the benefit of the good deed offered. The Prophet's famous hadeeth on this comes into play "Actions are by intentions, and you shall receive (the reward) for that which you intended."
Shirk Jahri (open) would be idolatry, or giving worship to other than Allah, whether a human being, animal, stone, teh Sun, Moon, even Prophets and Angels.
ps. You're right, I do not see any shirk in this video either.