When joining objects, one object must be chosen to join all the other selected objects too.
In this case it doesn't really make a difference which object that is, but if you had different modifiers or materials on the objects, blender needs to know which object's modifiers should be used on the resulting combined object.
Normally this is done with the Active object, which is outlined in yellow and in most cases is the last selected object. Note that an object can be active without being selected.
Right after running the cellfracture operator is a rare case where there is no active object. You need to define one by selecting an object, but after you have done that, that object is active until you select another object and it becomes the new active object.
In the tutorial he uses ⇧ Shift RMB on a already selected object (orange outline) to make it active (yellow outline) without affecting the rest of the objects. I'm not sure why this didn't work for you (are you sure the object's outline didn't change color?), but you can just as easily select all the objects after one is active, e.g. with box select (B) or if you really want to select all the visible objects, A.
Once you have your active object and selection, you can join them with ⎈ CtrlJ or the join button in the toolshelf.