If I'm reading the actual court documents correctly:

1. This wasn't an appeal. They had to make their motion to both the federal district court and the circuit court.

2. This was a motion for a temporary stay, not the actual case.

3. The rejection acknowledged the likelihood of economic harm to Anthropic but weighed it against the impact to the DoD. This isn't shocking and is how stays are meant to work: it isn't primarily a test of who is likely to prevail, it's primarily a test of what the risk to both parties is.