Am I really required to use the software Houdini to participate? 

or is it good enough if I make use of "Game Jam Starter Kit" asset?

Using the Game Jam Starter Kit assets in the game engine without using Houdini itself is permitted, but keep in mind that the judges will be looking for "Best Use of Houdini" when judging the games. Each team will also be required to list which tools they used and how they used them.