If this case was decided before a real judge, rather than Judge Judy, the impertinent party could be held in direct contempt of court (imposed summarily and punishable by penalties similar to a misdemeanor crime), after being given a moment to make a mitigating statement, but should not have have had the case summarily decided by the judge merely on that basis.
A judgment imposed on that basis without further findings of fact would ordinarily be reversed on appeal (unless the appeal was from a court not of record, in which case a new trial is held in a new court following every appeal in any case). But, a contempt of court award in that situation would be reviewed for abuse of discretion and it would be a close call as to whether a contempt of court finding would be upheld for that conduct which is close to an abuse of discretion at a minimum. It would depend to some extent on the sanction imposed and a $5000 fine would probably be considered excessive in that context.
Usually, however, arbitrators do not have contempt of court powers the way that almost all ordinary judges in the U.S. do.
On the other hand, while there are isolated reasons for invalidating an arbitration award, it would be an uphill battle to get an arbitration award overturned on this basis, although not impossible. An arbitration award must usually involve some good faith effort by the arbitrator to resolve the case on the merits even if particular mistakes of law or fact are not reviewable. Indeed, the most common reason that arbitration awards are reversed is the refusal of the arbitrator to consider all relevant evidence. The prevailing party could argue that this was a de facto sanction award rather than a true resolution on the merits and might very well win, but it wouldn't be an ironclad class.
Whether it is ethical is another matter that has two answers. At the level of did a judge give someone something that they didn't deserve, the ethical answer may very well be no. But, at the level of formal sanctionable judicial ethics, this would probably violate the duty of a judge to show judicial decorum and respect the process, although it would probably be a very minor offense resulting at most in a public reprimand.