This implementation is the opposite of this goal. They explicitly eschew this in favor of making something small. So, no error messages, no printer, no macros, none of the things that make lisp "real."
To the extend that BF is not real then this implementation of lisp isn't real either.
It can run some programs made only of exceptionally limited forms. You can, of course, build the components like integer addition and subtraction yourself in the least efficient way possible; however, how is this any different from the situation in BF?
They themselves also say this: "The code above is a LISP within a LISP within a LISP: three levels. You can use this technique to implement missing features like macros."
I'm not saying any of this to be critical of this team's implementation, more so to defend the notion that brainfuck is just as "real." Or, if brainfuck is "not real" then this particular implementation isn't for more or less the same reasons.
In the Lisp world, there exist small interpreters whose only job is to boostrap implementations. They are not used for developing any of the code they run; it is assumed to be correct. Handling of conditions that don't occur can be left out.
Definitely, this has its place.