The unanimous decision hinges on a couple of definitions. One is that the recall counts as a "measure" under Texas law. I don't think this is an obvious definition, and the court does not cite case law, but it is not unusual. California has stated that the recall vote (the "should the official stay or go" vote) is a ballot measure. I can't tell whether El Paso also has a two-step process (up or down on the official, followed by a replacement vote), but I know other Texas jurisdictions uses this form of recall.
The other big decision by the court is that the church is a corporation, and as such cannot make an expenditure to a recall campaign (it needs to use a special purpose committee). We've seen special campaigns finance laws for recalls in other states -- Arizona, Wisconsin and Washington -- so, not unusual there. The court then noted that the church had a link to petitions on its website, and since Brown and others took the fifth, took a negative inference on other recall related activities, such as paying for the petitions, using the church's facilities for signature gathering efforts, etc (all of these count as expenditures). The court flat out rejected the First Amendment arguments of the church, including an attempt to use the Citizens United decision.
The court threw out the signatures and ruled that the election cannot take place. I've seen courts stop recalls before, but I can't recall one tossed out based on donations to the committee (usually, in political recall jurisdictions, it has to do with the specifics of the signatures). That's not to say it hasn't happened, or hasn't happened regularly. California did throw the book at people who violated the campaign finance laws in the David Roberti recall, leveling an $800K penalty. But the state did not try to stop the recall.
For some positive news for the recall proponents, they should look to last year, where both Arizona's and Michigan's Supreme Courts overturned appellate court rulings and took strong defenses of the recalls, allowing the recalls to go forward despite some questions. Arizona specifically held that recalls face a more liberal substantial compliance standard. It should be noted that Arizona and Michigan have the recall on the state level. Texas does not.
The decision also includes a serious benchslap of the trial judge for an "abuse of discretion" in not stopping the recall, saying that he failed to apply the law to the facts, "hindered the judicial process" and noted that the court should "...not be swayed by public clamor or fear of criticism." And this was for not stopping the election.
It should be noted that El Paso requires (though I don't see it mentioned here) that the recall be held on a regularly scheduled election day (i.e. a primary or general election day). I believe this law would be a big asset to the recall proponents -- socially conservative voters who are against the domestic partners law that was the impetus for the recall are much more likely to turn out in the Republican presidential primary than liberal voters. What we've also seen in other states is that delaying the recall could push it off months (perhaps till November). This might have been a reason for the judge to push this election forward to the next stage.