So I watched Dungeons, Dungeons & More Dungeons today, and I took notes on what I saw about the game. Here's what I thought was relevant.
Use of a 38-sided die
Dungeons & Dragons uses 20-sided dice (called a d20), other Platonic Solids (d4, d6, d8, d12) and d10. There are other, more unusual numbers of sides you can have on a die, but they are generally novelty items and are not used in D&D. A 38-sided die is largely unheard of for any roleplaying game.
There is math involved, but the rules try to keep numbers low, and the math you do need to do is addition, multiplication and subtraction. Maybe dividing by 2.
Uses a Narrator
Yep! Dungeons & Dragons has one player act as a narrator, called a "Dungeon Master", who runs the world while the Players do things in it. Outside of Dungeons & Dragons, the term "Game Master" is commonly used. Other systems may have their own terms (e.g. "Storyteller").
Overly Complex Rules
D&D attempts to provide rules for the most common things you could want to do, so that you have something to refer to. Generally they try to strike a balance between being too complex and being too broad or unrealistic.
Because the creators of the game can't possibly think of everything, the Dungeon Master is given the authority to make a ruling to cover something not defined in the rules (usually, they will ask for a die roll and tell the player that the action will succeed if their roll equals or exceeds a certain number).
This is used (Depends on your group, though)! People use graph paper in D&D for mapping things out, either as the Dungeon Master, to keep track of where things are, or as the players, to keep from getting lost.
During one scene, it appears that they had some sort of dedicated game board in front of them. While graph paper might be used, game boards are unusual. There are dry erase mats that are sold, though.
Preparation Outside the Game
This is a thing. Game Masters usually want to be prepared so that they aren't making everything up on the fly.
D&D has a style of magic called "Vancian Magic", named after Jack Vance's Dying Earth fantasy novels. Generally speaking, wizards must prepare spells at the beginning of the day so that they can be cast later at a moment's notice. After a wizard casts each of these spells, they cannot cast them again until they are once again prepared.
That said, there are games where you can cast magic all day long. Still, it's much more common for magic in RPGs to have built-in limitations of some kind for the sake of game balance.
Eating Brains to Gain Intelligence
Thankfully, D&D doesn't do this. There are Mindflayers, which are monsters that eat brains and have mindcontrol themed powers, but they don't gain Intelligence when they do.
Die Roll Determines What Occurs
Not usually. A player first says what they want their character to do, then they roll to see how effective their planned action was. The dice do not indicate which of several actions might occur, just whether the planned action succeeded.
Related to that, it's considered bad form to roll first and then announce what the planned action was (some less honest players have a bad habit of rolling, seeing a poor roll, and then saying they were "just playing with their dice"). Many Dungeon Masters would tell you to roll it again if you do that.
F(something) Cardboard Legitimate Outdoor Role Playing
This wasn't part of the game they were playing, but Live-Action Role-Playing is a real thing that people do. Usually not with cardboard, though.