I don’t feel like I could give a clear explanation of いる・ある vs. です, but you can use both ここです and ここにいる・ある to point out the current location of something. I would say ここにいます in many situations though about my own presence but ここです is a simple fact and probably an appropriate response to some things (reporting where I am, reporting that I’m present maybe)
です is more about the state in which something is though.
Similarly you could also say どこにいますか or どこですか but I usually encounter and was taught the latter…
In the expanded version of the lesson OP was watching (the site has a transcript which is their whole lesson on [place]です) they don’t say it’s the proper way to say it, they just say it means that. Because it does. The lesson is about asking where things are.
Am/to be just encompasses just about everything in English.