I never played 4e, but I wonder if the difference can be tracked by looking at the Acquisitions Incorporated game, which started off as a 4e game and then moved to 5e as it became this 4 hour show that would only happen 3-4 times a year to a live audience. Those games are really light hearted and silly; basically every character is a vehicle for the player to make jokes, and this makes it entertaining. There's nothing specifically "medieval" about it except maybe in a ren faire sort of way, and in fact every time a new product comes out they take the whole game and move to to a different setting without too much difficulty. It is very self referential (the whole idea of an adventuring group as having a "brand" and "interns"and what not). The players don't really need to know the rules, and it seems that the dm can know the rules but should often ignore them and hold on very lightly in general. Similarly, the dice camera action game: I listened to it a little bit, and it seemed the players were running a bakery with their pet owlbear and would occasionally have a huge combat where they would win and if someone died they were resurrected by the next session. Again, they were playing one of the official adventures, but in a very hand-wavey way that focused on the characters.
So, is "goofiness" a style of play? I think when you start to take any element of 5e too seriously--the mechanics, encounter building, world building/lore, character creation, etc--it becomes less and less interesting as a game. It works best when yes, half the players don't know the rules but its ok because you can just make it up and it works out fine, your party is an half elf, a tiefling, a tabaxi, and a kenku, they have patrons and gods that they barely think about, they can't really die, and they are teleporting and plane shifting around to different settings in a story full of plot holes; don't worry about it, says the game. Also, you're not going to play for another two months because of scheduling issues and by then everyone will have forgotten everything about the campaign.
fwiw, I tried to watch some of the mcdm actual play and it was extremely boring.