Most gamers would agree that there is a relationship between tabletop games and videogames, but defining that relationship is tricky. When Super Mario Galaxy inspires Mike Krahulik to carve Styrofoam planets for a D&D game, we might call it romance. When Final Fantasy uses the Vancian rules popularized by Advanced Dungeons & Dragons for consumable spellcasting, we might call it theft. We might liken Jack Chick's assertion that D&D encourages suicide to Jack Thompson's accusation that videogames teach murder.
However, these relationships have no predictive value. D&D combat maps inspired the isometric playfield in Shadow Sorcerer, but that romance didn't really soothe the game's pathfinding flaws. ZODIAC: The Final Fantasy RPG directly borrows from its namesake, but it has never achieved the same breakout success. No amount of ribbing Jack Thompson and Jack Chick will predict the next gaming scandal.
The problem is that romance, theft, and other pithy parallels are just-so stories, ad hoc explanations that don't actually explain anything. They miss the nuances that make videogames and tabletop games simultaneously similar and different, so you can't reliably leverage them for the next great idea. Fortunately, just-so stories are hardly a new problem and they certainly aren't limited to games. Biological science tackled this sort of storytelling with evolutionary theory, and it's possible to lean on that work to help understand that common heritage is the tie that binds tabletop games to videogames. If you trace their pedigrees back far enough, both grew from simulations.
D&D and all subsequent tabletop games have roots in war simulation. As early as the 19th century, military officers were using figures and topographic maps to simulate battles. They used dice to determine battle outcomes and war games helped train new officers. These simulations fascinated 19th century military men but in the 20th, it spread as a hobby amongst civilians. In Lake Geneva, Wisconsin, one group's familiarity with war games and a fascination with the fantasy stories of Jack Vance and Robert E. Howard (Conan) eventually became Dungeons & Dragons.
Modern videogames also have roots in war simulation, if a more fanciful sort. Although other electronic games preceded it, the first widely influential game was Spacewar! Steve Russell designed the game to demo the processing capacity of the PDP-1, a 1960s era computer that would barely fit in a kitchen. Being science-fiction geeks, Russell and his team decided to simulate a space battle, complete with inertial physics, a central gravity well in the play field, and two armed spaceships. The idea caught on, inspired copycats, and ignited the game industry.
To see the impact of common heritage between videogames and tabletop games, consider Darwin's finches: a common ancestry that branched in different environments. Darwin observed that, although finches inhabited all the Galapagos islands, the finches on each island were distinct species. He theorized that their modern differences rise because they occupy the same niche in separate environments. Videogames and tabletop games have also developed on what amounts to different islands. Videogames developed to run by CPU, whereas tabletop games were run by people. Speciation makes each kind of simulation different, because each environment has different resources.