I found this indiegogo link from 7 years ago which gives a little more background. Its not quite as horrible as the picture suggests, I think.

There's some FAQ and Comments that give some background, like this one:

Rier Esor 7 years ago I’ve been asked by a few people: why do we need reefill water stations when there are water fountains around NYC (if you look hard enough!) and we >all have tap water at home? What’s my best answer?

Patrick Connorton 7 years ago PROJECT OWNER We're also working with New York City and the Port Authority to map free public bottle filling stations around town -- these are usually in or near >parks but, unfortunately, need to be off six months a year to avoid freezing and can be challenging to maintain. Reefill is a natural complement to >these fountains, filling in the gaps in parts of town where it is impractical or cost-prohibitive to install a water fountain.

So it doesn't sound like these were replacing existing free water fountains, but instead offering free (and paid) water in places never offered before by generating revenue from the paid water to support the installation of any water (including new free water) in places that had none before.

It also looks like the project died in 2019.

All I could find were articles from 2017 and I haven't heard of it before, so I'm gonna say it's not a thing any more.