There are multiple levels of desperation that determine how far you should play according to their rules and how much they should play to your rules or be ignored.

Option 1, Desperation level low: If you are not desperate for a job, just don't work with them. Preferably let them know that creating a Word file is too much of a hassle for you. This gives them the opportunity to back off from their demand and accept your PDF or at the least it is some feedback for them to think about changing the way they work.

Option 2, Medium Desperation level: If you somewhat need the job, get LibreOffice (or another free Office tool) and produce a Word (docx) document with it. Tell them you used that software instead of original Word because you don't privately own a license and that therefore it might look garbled up when they look at it with their MS Word. This means they get something that may directly work for them or need some low to medium effort to fix the formatting. But it's a compromise with a good chance for them to be satisfied or ask any missing information lost in the transformation directly. They might also decide to go with your PDF option and, again, it provides feedback to them that their way isn't the fully accepted standard.

Option 3, High Desperation level: If you really need the job, get an MS Word license and copy your CV. There are some tools that provide an auto-generated skeleton from a Latex source, I think, but last time I checked, they still required some manual work.

Personal Opinion: Recruiters provide a service to companies and to workers. They can only flourish if they keep both happy. Their profession is to smooth out the initial contact so the ones that fit each other find together without the hassle of establishing first contact. They should be good in communicating to both and they should know that there are these oddball engineers who don't use the typical marketing business toolchain, as they have their own preferred and established tool chain. Therefore, in my opinion, any recruiter that insists on such technical details is a bad recruiter (or he is in a very comfortable situation where he as too many good candidates already). He may ask for his preferred format, but he should always be able to accommodate (reasonable) choices of both a company or a candidate. It's exactly his job to translate between both! I'd simply move on, letting him know why.