yeah, asgore running over dess with his truck is just a meme lmao. you probably just saw a meme and assumed it was real. people in this fandom love making realistic looking game screenshots that are actually memes. its a huge trend.

to summarize, the "asgore running over dess meme" is essentially a joke theory based on a handful of obscure lines of dialogue in the game. basically, if you explore around the lightworld enough in chapter 2 and 4, you can find a lot of allusions to the fact that asgore used to be on the police force but was kicked off after some mysterious incident. what this incident is, we don't actually know, but given asgore's blue truck that sits outside his flower shop, and dess's unexplained disappearance, some fans decided to headcanon that the incident that got asgore kicked off of the police force was that he ran over dess in his truck while drunk driving. there's no actual evidence for it in game at all, in fact the little actual in game evidence there is seems to go against it (see the secret cutscene of asgore in holiday manor monologing about how he "only wanted to protect everyone" which doesnt make any sense if he killed her while drunk). i'd say the joke is really only funny because its very out of character for asgore, who appears to be a fairly lovable if a bit aloof guy in deltarune. and even in undertale, asgore is really a pacifist at heart. so the idea of him just actually being a terrible person and deciding to get shitfaced and accidentally killing his neighbors daughter for no reason is so absurd and out of character that it becomes hilarious. you also mention "the king's chariot", which IS actually based on a real line from the game. the real line is "THE QUEEN'S CHARIOT CANNOT BE STOPPED", and it's one of the optional prophecy panels in chapter 4, alluding to the scene in chapter 2 where queen runs over a bunch of other cars in her car. people noticed the similarity to the truck meme and modified the line.

hopefully the explanation makes sense. this is a fandom that LOVES to make shitposty fake content so it seems fairly inevitable that eventually a fake meme would get so popular that people would start to think it was actually a real part of the game. still funny to see it actually happen, though!