I've been reading (and really appreciating) the Q/A's on this site for quite awhile now, but this is my first foray into making a comment - so please forgive me if I'm off track.
You asked "How can I create something like it with Gimp, Photoshop or any other laptop application?".
I'm not sure if you are asking about the technical side of how the application might be doing this, or whether there's an application that you could use on your laptop to get this effect. If the latter, I've used a free program called "FotoSketcher" a few times. I can't comment on whether it's more or less sophisticated that the Waterlogue app, or any other "painting" type photo app, as I haven't tried them. My sense of it is that it's a bit primitive, but nonetheless kind of interesting and fun to experiment with. You can choose from a number of different painting "effect" (e.g. oil, watercolour; textures or not) and then watch it "paint" your photo with these. It's slow (at least was on my computer), so I found it best to use a relatively small jpg rather than a large file as that would have taken forever. There are probably other free programs out there that do this kind of thing as well.