It's a great idea. It pretty directly re-humanizes the web.

Some marketing to consider...

Both "staring" and "strangers" gives it a disconcerting vibe, amplified by the dark background and the naked request to enable the webcam.

What about "See someone" or "See someone seeing you" or "See someone seeing you for a second", with a blue sky to start?

Then instead of emphasizing staring, just say something like "blink to leave".

Thus: "The webcam will show only your face, and then you will see someone seeing you. Blink to leave."

Also, in the detailed explanation, you might add that it is peer-to-peer, and no images are captured or stored anywhere else.

The "buy me coffee" link makes the site seem... incentivized, I guess. If you instead add that prompt to the information panel about you, I think you would still capture the appreciative few without putting off the many now triggered by pervasive tipping (kind of like early google text ads vs yahoo banner ads).