It's an old trope that people who love the fantasy genre also love chess. Here, for your reading pleasure, are some chess concepts I find highly useful as a DM (and, arguably, in other pursuits as well).
In the broadest of terms, "tempo" is simply the concept of time as a commodity. The idea is efficiency of movement. Do something simple that has a complicated effect. The difference, as a DM, is that I want to keep the ball in the players court rather keeping all the control to myself.
2. "Positional play."
The idea is simply to understand the value of an ideal long term position. Basically a move can be good in the long view even if it has no point in the short view of things. NPC's, magic items, and loose plot threads (whether instigated or neglected by the players) all have a way of proving useful in ways that you might not have originally intended - so, always keep them in the back of your mind!
Sometimes the hardest thing to know is when to let go of something - particularly NPC's and Villains. But, if you do it right, the return (in terms of story interest) can be very high.
Can you find ways to complicate the plot by means of the character's own wants and desires? I bet you can.
5. "Draw by Three-fold Repetition"
In chess, if you let the same position occur three times of in a row, the game ends. The lesson? Never let things stagnate.
6. Lasker's Rule: "If you see a good move, stop and look for a better one."
Same with RPG plots. In my mind this has pragmatic application to my previous post about finding "The Edge".
7. "Mikail Tal's Hippo Story"
I won't bother trying to fully retell the story, but basically, Mikhail Tal found himself in a tough spot in a high stakes championship match. The position was very complicated and he was unable to reason out the correct way to proceed. Suddenly he fell into an intense daydream about, of all things, figuring out how to remove a hippo from a swamp. He claims he actually saw the hippo floating in the middle of the chess board and became immersed in imagining complicated sets of imaginary riggings and pullies!
So what happened? Well, ultimately, he admitted to himself that there was no way he could intellectually solve the problem of the Hippo - it was simply too complex. As soon as he did so, the Hippo dissappeared and he suddenly, irrationally, just knew the correct move.
The lesson? Trust your intuition. In the end, your gut knows what is the best.