About Season 13 timeline: imo The Scorpion and the Frog was happening while GoT was airing so between July 17 and August 28. If not Dean's line makes no sense. It was probably late in the season so that way Patience can be back to school not too long after that.
Hi there! And that’s true, but I tend to give less weight to throwaway lines that are intended as fourth wall breaks, as well as Dean Snark, for stuff like this.
Dean: Well, looks like gun beats knife, so how about you hand over the safe, and then we’ll all be home in time to watch Game of Thrones.Shrike: I’m more of a book guy.
Which is both Classic Dean Snark, but also a VERY SPECIFIC fourth wall break, because as the superwiki says:
Richard Brake who plays Leonard Shrike played the Night King in seasons 4 and 5 of fantasy TV series Game of Thrones based on the books by George R.R. Martin.
More than anything else, that line was a shoutout to the actor who played Shrike, and a joke. He’s more of a book guy? Well, he literally was IN the tv version, so… the line was just there as a tip of the hat and a lampshade on who Richard Brake is in real life. So a sort of double fourth-wall-break, kicking through the SPN wall as well as the GoT wall with one neat kick.
Dean theoretically could’ve picked ANY well known tv series. He could’ve just said “We’ll be home in time for the eleven o’clock news.” But name another tv series that has as much pop cultural recognition as Game of Thrones. Maybe The Walking Dead? Which wasn’t particularly relevant to the plot of 13.08 (speaking as a writer trying to pull off the joke here), and wasn’t relevant at all to Richard Brake… and which they’ve also already referred to in order to poke the John Winchester/Negan thing in another fourth wall break back in 12.15. They’re unlikely to use the Walking Dead again for anything BUT a John reference.
But in-story, Dean took one look at Shrike, at the situation he’d found himself in with working for Barthamus, playing a strange strategy game against the demon while also being at the mercy of the others involved in this heist, and from what little Dean new of the reclusive collector they were sent to rob, and the parallels to 12.12 and their mission to take out Ramiel… There’s a LOT of familiar crap getting churned up in this situation for Dean… He doesn’t trust ANY of them, really (though he does come to trust Alice eventually, and he DOES figure out that Barthamus and Shrike both had a hidden personal agenda, but that Shrike was the more sympathetic of the two…). He just wants to play this game and get him and Sam out safely, in order to stop yet ANOTHER demon (Asmodeus) from getting his hands on the Macguffin Parchment with the spell to summon a nephilim, thereby putting Jack at risk.
It’s all very Game Of Thrones-y.
Not to mention, the character Alice/Smash shared a number of parallels to Charlie Bradbury, from her mannerisms and the circumstances under which they met right down to the end of the episode when they put Alice on a bus like they did with Charlie in 7.20. Alice even uses the line “Sorry, Charlie” while talking to Dean. And Charlie, in 9.04, watched season one of Game of Thrones with Sam and Dean. Charlie was searching for her own quest in 9.04, and referenced this:
Charlie: Saving people, hunting things, the family business? I am down. But… I was raised on Tolkien, man. I mean, where is all this? Where are my White Walkers and my volcano and magic ring to throw in the damn thing?
White Walkers? *points up to the paragraph where I described Richard Brake’s role on GoT* So in another way it was also a reminder/nod to the friendship Dean had with Charlie.
Do I think Dean literally was concerned about missing the broadcast of a new episode of Game of Thrones? Not in the least. I mean, It airs at 8pm local time in Lebanon, Kansas. Granted, we’re never told where Shrike’s home is, but we’re assuming it’s somewhere in the vicinity of the bunker, within a reasonable driving distance at least… So to get SUPER nit-picky, sunset in Lebanon, Kansas is after 9 pm in late June and July, and it’s already dark out when they arrive at Shrike’s property. So they already would’ve missed Game of Thrones.
Unless it was literally just a nod to the actor, so a nice little fourth wall break, and a joking reference to the sort of life and death strategy game they’d found themselves trapped in.
Oh, and one last thought… Does GoT even air on the same schedule in the Supernatural Universe (which has been established repeatedly to be fundamentally different from our “real” universe out here in SPN tv viewer land)? I mean, to throw in another scream-into-the-void-worthy moment from canon, their take on who the president of the US is at any given moment in canon… (please nobody ask me to sort through that can of worms today, this one is enough thanks :P). But really? Yeah, I think it was mostly Meredith Glynn making these rather pointed fourth wall breaks, as well as Dean being a snarky little shit in-story, and not an expression intended to confirm his evening tv viewing plans for that specific night.
ETA: ALSO! Patience was already confirmed to be a senior in high school when 13.03 aired. She would not still be going back to high school if it were already August. She would’ve graduated and been leaving for college. Because we KNOW that 13.03 happened no later than May 23-24 or so.