The product you are describing is the 4th Edition Dungeon Master's Kit
This was released midway through 4th edition's release and included a book as well as some maps and tokens. Unfortunately it is out of physical print. You can buy the book only as a digital PDF here.
There is no "Dungeon Master's Kit" for 5e that has been released or is scheduled to be released before Christmas 2014.
Keyword is "kit" which generally means a book, some dice, and some tokens/figures to aid in the visual representation of play.
The 5th Edition Dungeon Master's Guide will release shortly
The DMG will be out December 9th. It is simply a book, a big one, covering lots of rules and providing a ton of setting and optional rules for 5th edition.
4th edition and 5th edition are similar but different
Both tell stories about heroic adventurers but the framework they use to tell these stories and engage the players is different. There is a tonal shift in focus for the rules between editions. The 5e DMG is not compatible with the 4e books.
Buying all 3 books will ensure your son and his friends will be able to play the new edition.
If you do pick up the 5e Player's Handbook, Monster Manual, and Dungeon Master's Guide they will have everything they need to play 5th edition.
There are a few official miniatures out for 5th edition currently but they are not available online.
Wizkids partnered with WOTC to make plastic miniatures for 5e, but they seem to be only available in game shops. You may want to check out a local game/hobby shop as they have these or other fantasy miniatures that he could use.
However any miniatures your son already has are perfectly usable with 5th edition.