In this shot, a fellow prisoner is seemingly disintegrated or something. I'm wondering what that was. Was he being killed or was it a portal or something?
Nope, the consensus is that he's disintegrated. There are many time this is seen.
Among others the BBC confirms
It is in these early scenes – while Loki is being processed through the TVA's Kafkaesque bureaucracy, full of bored office workers sitting amidst drab 1950s-style yellow and brown decor – that the show sucks you into its delightfully absurdist tone and rhythm. A disgruntled jobsworth presents a stack of paper and asks Loki to sign off every word he has ever said. A grinning corporate mascot blasts off all his clothes. A fellow prisoner is disintegrated for not getting a ticket to wait in line.
Post Episode 4
It is now possible that disintegration is NOT the only option since...
Loki (our Loki) is apparently disintegrated but in a post-credit scene wakes up on a post-apocalyptic landscape with 4 other Loki variants.
Episode 5 update
It now seems that everything pruned by the TVA, timelines and variants included, is now dumped into a branched reality "at the end of time".
See LethalCarrot's answer for detailed information.
This is answered in episode 5:
When variants (or people or things) are pruned by the TVA they are not disintegrated or killed but instead sent to the Void, a place at the end of time where all time simply stops. The same goes for reset branched timelines which is mentioned below:
Ravonna: When we prune a branched reality, it's impossible to destroy all of its matter. So we move it to a place on the timeline where it won't continue growing. Basically, the branched timeline isn't reset. It's transferred.
Sylvie: To where?
Ravonna: A void at the end of time. Where every instance of existence collides at the same point and simply stops.
Loki, Season 1 Episode 5, "Journey Into Mystery"