The article does cover this. They have moderators that would keep things on track. Most of your interactions on a daily basis don't have moderators.
However, I'd also argue that in most cases these social group hierarchical roles aren't going to end up having a large influence on communication style: typically it's only if there's something pressing going on. (Or, as I've already described elsewhere, if someone is unfairly taking advantage, the negation of which is a condition for cooperative interrupting to work.)
Magic: The Gathering works like a computer (quite literally it's Turing complete). When you play a card or ability, it is put on a stack. After you're done, you need to yield - then the other player may play things on the stack too (but, they can only play "instants" - most other cards can only be played if the stack is empty). Then they must yield, and so on.
(In the 90s, instants meant to interrupt other spells were called "interrupts", but this name was dropped)
After everyone is done, things are popped from the stack in the reverse order they were played (like any stack). So if your opponent played something in response to what you played, their card resolves first, then yours. But if you played something in response to their response, your card resolves first, then theirs, then yours.
This would be very tedious, but in fact most decks have few instants and little interaction with the stack, so most of time you play a card I will just wait it to resolve and generally wait my turn to play. And famously, no card of MtG is allowed to mention the stack in their printed text: while the concept itself is intuitive, talking about the stack is a sure way to make a card overly complicated.
Final aside: I used the phrase twice, so it should be clear that the history of said game (again, Yu-Gi-Oh) is plagued with degenerate combos.
EDIT: Editing in this edit to acknowledge that there is a sibling comment with a valid nit that invalidates the reason I responded. In my defense, my slow phone-based composition took me so long I did not see it until this edit. I'm leaving it for the sake of hopefully any nascent game designer getting any insight, I suppose. Or hey, card game players getting their kicks thinking about card game mechanics.
Nit: The Split Second keyword ability is usually accompanied by reminder text which mentions the stack
> Split second (As long as this spell is on the stack, players can't cast spells or activate abilities that aren't mana abilities.)
https://gatherer.wizards.com/Pages/Card/Details.aspx?multive...
https://gatherer.wizards.com/Pages/Search/Default.aspx?actio...
Note how the waterhouse's link - https://gatherer.wizards.com/Pages/Search/Default.aspx?actio... - contains a bunch of cards that were playtested but eventually rejected (they are the black-and-white cards with just a rough sketch in place of art), presumably because of the high bar that stack-fiddling cards should meet
And I'm fairly confident these semantics exist in many cars games. Unstable Unicorns had the neigh card. Uno has the rule of declaring uno. (Where you can interrupt the next play by calling uno to force the last player to draw a card. Note that this is a very specific time you can interrupt play.)
This is actually my single least favorite part of magic compared to yugioh, and I've played both a ton. Instead of a stack, yugioh has a similar first-in-first-out concept called the chain, with two major differences:
1) Every time you place a card on the stack, you yield to your opponent, who can either play a response or yield back to you, and this goes on forever until both of you have yielded without taking an action
2) cards have "spell speeds" of 1, 2, or 3 , where you can only chain an equivalent or higher speed card - this means unlike magic, you can pile up multiple sorceries/spell speed 1 cards into the same resolution queue
Both of these encourage a ton of interaction on the stack/chain, and often times yugioh games are won or lost as the result of a resolution or 5 or more cards and effects piling up and resolving, which is a relative rarity in magic outside of a few combo decks or infinites. Conversely, yugioh also presents a lot of powerful defensive options for interrupting degenerate combos, usually at a high cost.
> Not everyone is well versed in how those semantics play out
I would argue that this is not necessary: just watch younger people who are friendly with each other discuss something: what I'm describing is a natural mode of communication. AFAICT it's just overridden in certain cases when people are taught "never interrupt someone speaking" or something along those lines.
But I would be curious if you could lay out the tradeoffs with instant plays in the card game semantics you mentioned.