I do think that Dungeon World has an OSR vibe to it. I don't think that it plays like OSR, but it clearly was designed with OSR in mind. OSR was in full swing at the time of its making. Sage LaTorra and Adam Koebel definitely dabbled in the OSR space to various degrees. I believe that Adam Koebel has even said that some design decisions (e.g., race restrictions in playbooks) was written to evoke these older, pre-WotC editions of D&D. So it may be more accurate, at least from my perspective, to say that DW was inspired by old school nostalgia.
Now that I have a bit more time, as a bit of an addendum to my post here as well as picking up something that
@Malmuria was asking in regards to comparing 4e to DW:
While DW does have a bit of an "OSR vibe," there has also been something quite appealing about DW for 4e fans. I don't exactly think it's some grand coincidence that DW (to one extent or another) has been picked up by a fair number of 4e enthusiasts on the forums: e.g.,
@EzekielRaiden,
@AbdulAlhazred,
@Manbearcat, myself, and others. I also don't think that it's a coincidence that some of the creators and modders for Dungeon World -
A Sundered World* by Awful Good Games and
Stonetop** by Jeremy Strandberg - also came out of 4e.
*
A Sundered World essentially imagines if the gods lost the Dawn War.
** The Marshall playbook is a reskinned Warlord. The deities of Stonetop hybridize real world gods with Dawn War gods: e.g., Tor (Thor + Kord), Helior (Helios + Pelor), Danu (Danu + Melora), and Aratis (Athena + Erathis).
I would personally love a fantasy PbtA or FitD game that leaned heavily into the themes of 4e, the Dawn War, and the World Axis mythos (with the serial numbers filed off, of course).
Is there a good YouTube PtbA channel I could watch to see it in action?
Reading back through this, I'm not sure if anyone answered you.
Your question is a bit like asking whether there was a good channel for seeing OSR in action. The Gauntlet talks a lot about PbtA, and they do podcasts for their plays, but I'm not sure if you can "see it in action" on their channel.
It would probably help if you pick a game that interests you. It will make it easier to narrow down the range of possible channels or streams. Avatar Legends (Avatar the Last Airbender), Masks (teen superhero), Stonetop (a Dungeon World hack for iron age "hearth fantasy" where the village gets a playbook), Monster of the Week (supernatural monster-hunting), Urban Shadows (PbtA's Vampire the Masquerade sorta) are all pretty good games to look for on YouTube for getting a grasp on PbtA.