The judgment is not lengthy, nor does it break new ground. Indeed, the Chief Justice of the CMAC relied upon a similar rationale described in one of his earlier decisions, R v Royes, 2016 CMAC 3.
The decision in Thibault turned on the third part of the 3-part test regarding the such applications, established in RJR-Macdonald Inc. v Canada (Attorney General),  1 SCR 311. The Director of Military Prosecutions (DMP) acknowledged that the first two parts of the test - (1) Is there a serious question to be tried; and (2) Will irreparable harm result if the stay is not granted? - were met. The decision turned on where the 'balance of convenience' lay.
The Chief Justice observed that the third part of the test turned on two components: public safety and public confidence in the administration of justice. The Chief Justice rejected the application principally due to the second component, holding, at para 11:
The facts of this case are somewhat similar to Royes, supra (serious sexual assault; no risk of flight and the appeal only bears on a constitutional question). I reach the same conclusion herein as in Royes for the four following reasons. First, the events that resulted in the conviction date more than ten years ago. Second, the complaint was brought to the attention of the civilian authorities in 2012. It was only the military justice system, which took the complaint seriously. Third, at the time of writing these reasons, the Supreme Court has not yet decided whether it will grant the application for leave to appeal in Edwards et al., supra, which is the basis for the motion herein. Finally, this Court has pronounced on this issue five times, in nine appeals, including this appeal. In light of these observations, I am of the view that a thoughtful and dispassionate individual, informed of the circumstances of the case and respectful of society’s fundamental values would expect that the judgment of this Court be executed in a timely manner. The time has come for the execution of the decisions of the Court Martial and of this Court, in particular given that the Supreme Court of Canada has not yet pronounced on the application for leave to appeal from the decision of this Court in Edwards et al.
A reasonable person may disagree with the Chief Justice's conclusion. From my perspective, I would contend that the delay in prosecuting Sgt Thibault argues as much in favour of granting the stay pending a Leave decision as it does a rejection. If Leave is eventually granted, and an appeal before the SCC is successful, there is little that can be done to compensate Sgt Thibault for his loss of liberty. A reasonable person, informed of all of the relevant facts and law, would likely conclude that a delay of a few months to ensure that a person's liberty is not infringed in contravention of the Charter, suggests that the balance of convenience favours the Applicant. However, it is unlikely that any reviewing court would interfere with the Chief Justice's conclusion.
That said, the reasons for the decision are notable in two ways other than the individual impact on Sgt Thibault.
First, the Chief Justice noted that the SCC still has yet to decide on the Application for Leave to Appeal in R v Edwards et al, 2021 CMAC 2 (and several other related judgments that parallel Edwards et al). It has been over four months since the materials for that Application were submitted to the SCC. Notwithstanding that, as the CMAC judgment in Edwards et al was unanimous, the Applicants and putative Appellants do not have a right of appeal, the issue regarding the independence of the military judiciary is an important issue and one that has not been fully tested before the SCC. One might perceive a subtle criticism regarding the delay by the SCC in making a decision regarding the Application for Leave to Appeal.
Second, note the comment from para 11: "... the complaint was brought to the attention of the civilian authorities in 2012. It was only the military justice system, which took the complaint seriously." Again, that comment can be viewed as a subtle (or perhaps, not-so-subtle) message to the Minister of National Defence regarding her direction that all matters of criminal sexual misconduct arising within the context of the Canadian Forces must be referred to civil courts of criminal jurisdiction. Note, too, that despite this supposed direction (including valid questions about how that direction was conveyed), civil police are not uniformly accepting responsibility for such investigations and DMP is still preferring some matters of criminal sexual misconduct to court martial.