You can record people on the street with say your phone if you hold it yourself, but actually mounting a surveillance camera anywhere in public domain (except a dashcam) is only allowed in two cases. (1) people are adequately warned before-hand that there's a camera. (a warning sign will do, but a tiny sticker wouldn't, hidden cameras thereby can't be legal in any case) or (2) the camera doesn't film actual people. (e.g. bird watching, a live internet cam that watches the traffic or weather, or a busy square where the camera is zoomed out so much that individual people aren't recognisable).

Security cameras in public areas fall under similar conditions, but of course most of them are on private property where there are different rules. However, a shop is also public domain, despite being private territory, because shop owners open their doors to the public. So here, too, cameras surveillance must be communicated, too. (which can be the camera being very openly visible, a monitor showing camera footage indicating there's surveillance, signs, or e.g. a warning on the ticket of say a concert).

In short, what he did wouldn't have been allowed as it appears like he built this camera, 'hid' it (or didn't position it so it's easily visible to all), and didn't inform those being taped that they were being taped. That wouldn't have been allowed here, and I wouldn't be surprised if Dublin is similar. The solution would've been easy, and perhaps those taped e.g. ringing all bells wouldn't have if they knew they were being taped doing so.

What he did after, holding a phone and walking around, was completely fine, though.

But that's taping. Publishing (e.g. in a livestream to all) isn't always allowed. The law says it mustn't damage the 'reasonable interests' of a person, which refers to privacy issues. It's a bit vague what this means but I can easily imagine 'reasonable interests' relating to privacy meaning for example arguing with your girlfriend. None of that happened for the OP though, so his livestream was fine.