So with some investigation it turns out SMART Notebook 11.4 requires Ruby 1.8 to work. Except installing Ruby 1.8 from, e.g., Homebrew doesn't work. I guess SMART had statically linked Notebook 11.4 against the particular Ruby library that was distributed by Apple.
A bit of research online turns up a post describing the same problem and the solution: copy Ruby 1.8 from a pre-Yosemite Mac over to Yosemite in the same directory.
The directory is
Someone even made an installer and posted a link in the comments in that post, although I can't say whether you should trust using that installer... Not feeling comfortable using that installer, I dug up an older Mac and zipped up the 1.8 folder from the above directory and copied it over to my Yosemite machine.
Leave a comment here or message me if you want a zipped copy of the Ruby 1.8 folder. Or else if you feel comfortable with using that unvetted installer, then go download it from that comment.
Problems with this fix
Note that this method of making SMART Notebook 11.4 work will make the program less stable. I've had crashes from time to time. It also makes the toolbar unusable, and in fact, it won't even show up on the screen! So get used to picking tools the long way via the menubar instead.
I do wish there was a better software solution to what I'll call the "Projector Transparency Roll - Writable (50 feet)".