People can refer to themselves as Mrs, wife or married, when the widely accepted definition of the term does not fit them. That is their choice, but not surprisingly, many people will be slightly confused/surprised by it, in the same way that they would be if anyone used any other widely used term which has an accepted definition incorrectly. Most people won't be annoyed by it like the OP or even give it much thought, but will be rather surprised, if it someone they know, rather than just a stranger in a shop etc.
People on here have given reasons why they do it. Some make sense to me and some don't really, but it is their choice. People who are legally married don't have any control over who uses the word and who doesn't , in the same way, someone who is employed cannot prevent someone who isn't employed saying they are, or someone who does one job, referring to themselves by a different job title, or someone who lives in one town saying they live in the bordering town etc etc. With all of these, apart from in legal situations or job interviews, people might just raise an eyebrow and wonder why someone would do this briefly, but that would be all. Same on here.
Personally I think that words and their use do matter. Sometimes I find there isn't a word I like to express something, but I don't totally misapply an alternative word which means something quite different. Language is and has to be a common framework for it to work. Yes, it evolves over time and it maybe that another word for people in long term unmarried relationships appears, but until it does, the ones such as 'partner' 'other half' or 'my man' etc which have clear meanings, seem better and importantly accurate.