Hi Dan,
Kosovo wants its independence. In the early 2000's, the UN helped it; "under UN supervision, Kosovo developed the structures of an independent country." Also, the population is now 9/10 Albanians. with less than 1/10 Serbs.
www.britannica.com/place/Kosovo
So, even though there is disagreement internationally, I would tend to consider Kosovo a country.
btw, this is an important question and I appreciate learning more about Kosovo. The video you posted is very informative; that more UN countries voted against Kosovo independence than for it. Do you know why so many countries were voting against Kosovo independence, was it to help Serbia, as the video mentions?