Specific performance on residential real estate? Well...
Specific performance is a REMEDY, which means you'd have to win the underlying cause of action. Its likely you COULD win a breach of contract claim -- maybe even fairly easily -- but it will take a while. There will be a TRO issued (best case) and then a hearing to extend it (2-4 weeks); IF granted (and its no sure thing), then discovery, pre-trail motions, and trial. A year in the absolute best case.
If the trial court rules that monetary damages would suffice, then the case is essentially over. Yeah, the Plaintiffs win and get damages and attorneys fees, but by then the house they would have bought had they moved on in the first place will be priced higher. In fact, due to this, the court may not grant an injunction and then the case becomes much trickier. Absent solid legal bases, appealing to the Court of Appeals regarding spec. performance and an injunction isn't a good option.
Remember, if you don't win the underlying contract case, you will not only get specific performance (duh!) but you'll be out thousands in attorney fees plus whatever you lost by waiting on the other house. They could also agree to sell you the house at any point under the contract terms but not pay your attorneys fees. Then it gets very fact specific as to whether you'd even want to continue the case -- in other words, they were holding out for a higher price (not good on their part) or they wanted to stay in the house (much better for them -- and once the property is sold, the defendant -- the original owner -- getting a summary judgment on the remaining contract claims and damages not settled would be very high). Also, if they settle on the house and you get it, collecting on any future judgment (as stated above) would be much more difficult. Kinda a mess if you ask me.
But don't take my word for it. Maybe they can spend $400-600 and get a consultation from a board cert. residential real estate attorney who's done something like this. If they do that, please update.