Leave the soldering iron out for now, just get a multimeter. With this set, he has all necessary items to get him started. Once he knows what he wants to build, he will need more stuff, but what the stuff will be depends on his projects.
The additional breadboard (take one with 700-900 holes which is about twice as big as the included one), wirecutter and wire is welcome but not crucial.
For the soldering iron, some additional stuff like solder, desolder braid, and other stuff become necessary too and it's hard to figure out what is the right model. Once he knows what he wants, he'll know what fits his needs best.
Korman