Well semicolon lets you put two command on one line like this:
date ; uname -a
And $( ) sets x to the output of the command so x=`date` and x=$(date) do the same thing.
What the posted command is trying to do is to set x to the path of the get_tape routine. If get_tape does not exist in either place, x is null. If get_tape exists in exactly one of the places, x is that path.
But if get_tape exists in both places, x will be a two-line value with both paths in it. I wonder if the author of the code realizes that. Maybe that's what he wanted. Restricting the value of x to a single line would make this ugly construct even worse:
x=$([ -x /etc/get_tape ] && echo /etc/get_tape || { [ -x /abc/prog/bin/get_tape ] && echo /abc/prog/bin/get_tape; })
Personally, I think this really calls for explicit "if" statements. Then the code is much clearer, and much easier to maintain. But sometimes it is fun to crank out these opaque one-liners and I'm not really in a position to be casting too many stones here.