I actually do have a lot of exposure to patents, and I know everyone uses DocX already. I'm just saying that that web page doesn't say why they chose DocX, only why you should use DocX.

Sure it does. I'll give you it does not say why they chose it over other alternatives which I'm thinking is what you are looking for. Are there really any alternatives? The only real alternative I can think of is OpenDocument Format and I don't consider it alternative. As they say on that page, 80% of their users already deal with DOCX so 80+% of them will have to convert to ODF. I can't imagine ODF having any sort of benefit worth requiring most people to convert their documents before sending.

To me, the salient question is why is the government officially adopting a proprietary file format? Why is it important to optimize for the trivial convenience of patent applicants?

It seems more like rationalization than reason.

Isn't docx technically an open file format? https://en.m.wikipedia.org/wiki/Office_Open_XML

That's a standard for a file format, but that doesn't necessarily mean it is a free/open format. I don't think the FSF, for instance, considers it open (maybe because of patent issues). I'll leave that for you to decide, but just mean to suggest a standard doesn't automatically mean free/open.

Interestingly, a section in the wiki article linked mentioned the standard proposal was controversial because ODF already existed (and ODF was considered less complicated as a specification).

Nevertheless, good point. It depends on what you mean by "open".