Is It Acceptable to Contact the Professor of a Publicly Uploaded Lecture?
Of course it is acceptable. But you also might not get a reply. The professor has to prioritise their actual students over someone who saw a Youtube video, and they are generally busy people that may not have time to respond to your question. However, they will not find it rude that you ask. You can find most professors' email addresses by simply Googling their name anyway.

To maximise the chance that you will get a reply I suggest writing your question in the most concise way possible (hint: not the way your question here is written) and in a way that clearly indicates that you've understood the basics in whatever field the lecture is about.