They can, and it can even be enforceable - but remember (a) its not a real court and (b) a lot of what is seen will probably be staged.
I've not seen this show, but by way of analogy, look at "Judge Judy". The cases may be real, the people may be real, the rulings may be final, BUT NOTHING IS AS IT SEEMS. For a start, the people are paid to be there, the court is not actually a court, its Arbitration and, to me the funniest part - The studio pays all judgments - which means when JJ goes hard on how bad someone is and makes them pay to teach them a lesson - its actually the studio that pays. (There are also strict limits of the maximum amount).
Extrapolating out - I believe that these cases will be a "Guilty/Not Guilty" answer, rather then setting a judgment amount, and the parties will most likely have agreed - prior to the show - to accept the verdict as binding - probably for some compensation. Expect it to look real but be smoke and mirrors. If its anything like Judge Judy, record and read the credits at the end - In the case of Judge Judy it actually tells you how you are being scammed/entertained!