The plot revolves around a wargames scenario. There is for some reason an alien race that is really good at war strategies. There is an advisor from that race on the enterprise.
The advisor is a massive dick. However he’s also somewhat legit. He beats data at some strategy game.
The enterprise is set to fight a decommissioned federation ship. Half the crew comes over there. It’s led by Riker. Wesely is also over there. He snuck his dilithium science project aboard. He tells Riker about it. Riker is happy, because it’s enough dilithium to give him like a second of warp. He thinks he can use it in a surprise attack.
The science project itself isn’t super complex. LaForge was mildly impressed when Wesely told him about it, in a way that made it feel like he’s smart for his age. He started the entire project like two weeks ago.
Anyway in the middle of this the ferengi show up. This is one of the times they aren’t complete jokes. They start attacking Riker’s ship because they think it’s valuable or something. The enterprise can’t easily stop them because they are carrying dummy rounds. Riker ends up using the Dilithium is some sort of bluff to beat the ferengis.
The episode ends with Data and the alien strategist playing the game again. The strategist gets upset and rage quits. It’s revealed that Data realized that last time he was playing to win, so this time he was playing to not lose. He basically got the alien into a stalemate.
There are also a million other reasons why the Burn doesn’t make that much sense. The Klingons use Trilithium. The Romulans used a contained singularity. In Voyager we saw a number of potential non-dilithium alternatives. One of them was a glorified slingshot.
There’s also just the thematic implications. Star Trek has always been portrayed as this big diverse galaxy. There are a ton of alien races running around doing weird things that we only grasp the surface of. There are even more alien races we’ll never meet. There are races that have technology beyond our comprehension, and races that are effectively Gods.
I think the writers handwaved the entire thing away so that the Burn technically doesn’t break canon. Just like La’Rell winning the chancellorship is canon. However it feels almost antithetical to what we know about the setting.