Some courts make no distinction between various forms of extraordinary writs, and this may be the case in Florida. In Washington, this error would be handled as a petition for a writ of mandamus, but possibly as a writ of cert. The precise form of the writ is not important as most appellate courts will treat the application for a writ as simply a request for extraordinary releif in whatever form is available under the circumstances. Regardless, if there is a valid arbitration clause, the judge erred in his decision. As for whether the plaintiff's bar tends to be favored by the courts; in this case, the defendant's attorney is likely not too upset either since their fees will be considerably higher with a trial than in an arbitration.
As for the arbitration clause itself, if it has the "arising out of or related to" language and given the courts enormous preference to construe questions of arbitrability in favor of arbitration, arbitration would be the appropriate course for this case; assuming there is a valid arbitration clause.
Believe it or not, I am not an attorney, but I know this stuff better than most attorneys. If you want to discuss RICO and Civil Rights actions, I am most well versed in those causes of actions as well since I am involved in a huge case that will make national headlines once I find an honest judge. In case you are wondering, The Washington State Supreme Court makes the Florida Supreme Court look like amatuers when it comes to ignoring the law when someone goes against the government or a judge within the legal system.