So, after a bit of research:
An interesting conversation is happening on the subject, but most people haven't even googled what's happening.
The tweet is missleading. The paper will continue being printed, just less often. They are changing the print to monthly.
Also, the Wiener Zeitung is used as the governmental newspaper and it's going to continue online.
Additionally, the paper is financed by a mandatory tax from all companies in Austria. There was apparently a push against the physical form of the newspaper, as it costs everyone a lot of money for a daily print of something that's "50% useless updates for corporation updates that can be done online".
I'm a fan of this type of financing though. BBC is usually a good enough source for news, that I can believe enough (you always have to have in mind they are a liberal, pro-british source), because they are not sponsored by a single corporation or just the government (it's technically a corporate tax that the government then transfers to BBC, but as far as I know the law cannot be changed, so the government MUST pay them, no matter how much they hate it).
We need to have a system for independent newspapers and this type seems to be the best. Financed by the people for the people.