My current employer does this.
You're sat in the conference room, given a machine that has a screen monitor program running, and a set of tasks to perform on the code. You are told where to find the code in the introduction on the sheet of instructions. You are allowed to use any resource via the computer (so nothing you've brought in like a phone or laptop is allowed; basically, all work has to be "shown"). Then...go.
Outside the room, the dev team watches the process. We want to see how you go about each problem, what resources you use, etc.
It's always surprising the number of people who go for an hour or more and do nothing. Just sit there (or seemingly sit there - there's no keyboard or mouse activity).
When I interviewed, they actually gave me an online test; the job was supposed to be for javascript, but the online was in PHP (which my prior position used, and I had been using for years). Passed that, and came in for the on-site part. I thought it was odd that they first tested me for PHP. Did a bit of face-to-face interview, then they wanted me to do the watched javascript portion (single page app).
I first sat and read the problems, formulated some possibilities in my head, then jumped in. 30 minutes later I was done, and popped open a new file to write something to that effect (figuring if they were watching, they'd come back in). I sat for several more minutes, then they came back.
"How's it going?"
"Alright...umm, hey, I'm done."
"No way! Are you serious? Are you sure?"
Odd...
"Yes."
Apparently they had never had anyone finish the test that quickly, and get it completely right - especially someone who also had PHP skills, and had already demo'd them in the first test, which was also done correctly. I found this rather odd, as neither test was that particularly difficult.
Apparently, though, it's not uncommon in our industry. I'm not sure what to make of that...