They ask for a resume and tell you when to be there.
You show up at the appointed time with the resume. After waiting half an hour. a secretary hands you a generic Office Depot tear-off employment application.
After another forty-five minutes to an hour, you get to see whoever's in charge of hiring. They're looking at the Office Depot sheet, and about half the time they don't even have your resume, which was probably round-filed by the secretary.
The hiring person isn't sure what job you're applying for, so they leave the office to consult with someone else. Twenty minutes later they return and either tell you they're not hiring, or they'll call you next week. (they don't)
My usual response was to send them an invoice for two hours of office workflow consulting at my entirely reasonable rate. None of them ever paid up, of course, but they stole two hours of my time.
To me that means their hiring process is extremely formal and not worth my time.
What's wrong with .docx format? You can create it using open source office software. In my experience most forms are smart enough to parse .docx just as well as the obsolete .doc.
Besides, what other formats do you want them to accept? PDF, sure, TXT, sure. It seems silly to avoid word documents.
I write my CV in HTML, as that's just the easiest way to get my CV to look exactly how I want it, and then "print" it to a PDF in Firefox. I also have a little JavaScript to redact personal information if I add "#redact" to the URL, and send a PDF of that too to recruiters after I noticed that a recruiter had completely massacred my pixel-perfect CV that I obsessed over by copy/pasting it in some ugly crooked layout and sent that horrible thing to companies :-/
All of that said, I haven't used recruiters for many years, but back then my "redacted" PDF solved the issues for me.
Any recruiter who trusts their clients so little is probably not worth your time, however