When Missy turns into a "Ninja Turtle Princess of Power" as her Dungeons and Dragons character, the theme song from the 1987 animated series is heard. Chuck Lorre, the creator of this show, wrote that theme song. The "Princess of Power" part is referring to the She-Ra: Princess of Power (1985) cartoon series from 1985.
In this episode, Sheldon plays Dungeons and Dragons, which his older self is shown playing in The Big Bang Theory (2007). In The D & D Vortex (2019) (Episode 12.16), he and his friends try to crash Wil Wheaton's game involving celebrity guests.
In the board game Dungeons and Dragons, the Dungeon Master (DM) makes decisions based on die/dice number rolls. When Sheldon's mom asks him for a hug, he rolls the die (which looked like a D20, aka 20-sided die) and decides it's okay to hug her based on the die roll, whatever that turned out to be and whatever he decided would be the pass/fail roll of the die.