Someone has pulled a sample motion of this type off of PACER (the public access Internet portal to civil filings in federal court). The example is more formal and structured than a lot of state court motion practice would be, however (e.g. few state court's require or encourage motions with a table of contents and a table of authorities). This example is 36 pages long, and many states don't even allow motions to run for more than 10-15 pages without leave of the court to do so in advance. There is a New Jersey federal court example here which is also on the formal and fussy side (although, in part, because the motion isn't just an arbitration motion and is also raising several additional unrelated issues which if omitted would cut it in half). See also one here.
Another example, from a California state court, is closer to the mark for a typical state court filing. A court that handles residential landlord-tenant matters is probably even more "casual" and probably expects motions to get to the point more quickly.
The core content is probably solid, although it would have to be customized to reference the state law statutory and procedural rules rather than the federal rules of civil procedure, and to analyze and set forth the facts of your case rather than those of some random person whose pleading is linked.
This would also have to be adopted to state court practice standard, which typically uses different formatting for captions, signature blocks, whether or not line numbering is required, etc., and is often subject to other requirements. Some require that a certificate of service be filed as a separate document, while others routinely incorporate it in the main document.
Many state courts require that a proposed order be submitted with a motion as a matter of state or local court rules, a few states require a cover sheet to be filed with motions, many states require you to confer with the other side in the case and to recite their position opposing or supporting the motion, or something in between, before filing it, and some courts require you to notify them once the deadline for a response has passed, regarding whether an opposition has been filed to the motion's request for relief or not.
Similarly, some states courts require that motions be "verified" (i.e. have their allegations confirmed under oath) or supported by an affidavit setting forth the factual matters alleged in them.
New York State structures a lot of motions as "orders to show cause" in which the court preliminarily reviews the relief requested and issues an order telling the other side that it will do something if they don't file an objection showing good cause for the court not to rule in that way by a given day, which must be formally delivered (i.e. "served") upon the other side by a deadline. I don't know if New Jersey local motion practice is similar.
Many court systems also charge a "new case" filing fee for motions to compel arbitration that does not apply to other kinds of motions.
Ideally, you'd want to review some motions (about pretty much anything) to get a feel for how this is usually done in New Jersey.
