Were the dice needed for playing a paper RPG? Dungeons and Dragons? Yes!
Did Drake ask for dice, meaning RPG dice, and this was misinterpreted as regular dice? so he was upset when he got the regular dice so then proper RPG gaming dice (which can be really oddly shaped) were procured? Yes, and that's a
"Them" is "sides of dice."
Drake is a new RPG player who asked for dice for Christmas. One of his relatives thought he meant he wanted a board game and got him that, the large game box including two six-sided dice. This was not what Drake wanted, so he was unhappy. Then he opened a smaller box from another relative, which contained a set of RPG dice, and Drake was happy.
This puzzle isn't based off any one person, but I am part of a D&D group ("Drake" comes from the name of one of the player characters), and our DM got us all a set of dice as an early Christmas present. The set includes a d20 (20-sided die), d12, two d10s, d8, d6, and d4, or 70 sides altogether.
Nicely done everyone, especially Westing and Grip for the final tidbits.