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I suspect, from the tone, it is talking about those who are self-employed, not a bit of remote working whilst on holiday.
That article is not my main source, the Austrian embassy is. Under freedom of movement you are perfectly permitted to do a bit of work on holiday. As a third nation citizen, you are not permitted to perform any work at all while on a tourist visa. Even remotely for a UK company.
At this point in time its only possible to get a work permit to work for an Austrian company so you can't even apply for permission to work remotely while in Austria.
As jellybaby says, its actually the same in the UK for EU citizens.
Edit: Just to add some more weight to it, Mrs Hedge's company (a very large multinational) have consulted their lawyers and they have confirmed that it is impossible for a UK citizen to work remotely from Austria legally at this time.
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I don't think the article is particularly clear https://archive.ph/jxTOL
I suspect, from the tone, it is talking about those who are self-employed, not a bit of remote working whilst on holiday.