Considering the guys on the thread don't know MIPS is an assembly language, I think there's some projection involved.
Though I am not sure why an iOS developer would program in MIPS and not ARM. Maybe there's some sort of crazy Apple MIPS hardware I never heard of... Or they had to pick one architecture and they happened to pick the one that had nothing to do with her company.
They obviously meant in the post that she can program in MIPS assembly. And they shortened it to just MIPS. I wouldn't be surprised if the "Java" mentioned was actually Javascript.
There's a very high likelihood that the "Java" referenced is actually Java, since the college that they went to teaches Java as a part of the standard curriculum (or at least they did via UMass Amherst cross-courses a few years ago). With that being said, I agree that it's likely MIPS assembly being referenced because that's what most people mean when they say they can program for MIPS.