There are a number of PictoChat clones out there which is just as surprising as it is unsurprising.
However…how do they stack up?

This is probably the one most people default to. FroggieChat^A) is a supposedly faithful remake of PictoChat made in Unity (Strike 1!) that makes a number of changes to the PictoChat format.
First, the emoticons are just not a thing? It removed them fully, at least in the demo version so that sucks. Emoticons were replaced with tips and even a lot of symbols are missing.
Second, color. It has more colors which actually (allegedly) improve the PictoChat experience. There’s even a random ‘draw something’ prompt if you’re not creative or if you want to enhance fun. I guess they’re assuming PictoChat is a game…which, yeah.
Downsides include Unity, but the UI also keeps bouncing around. By which I mean, all the elements are constantly moving, aiding the theory that it’s being treated as a game rather than a chat application. I wouldn’t mind if I could turn it off, but no such setting appears to exist in the demo version.
Also, it’s local only. This is a massive dealbreaker for losers like me, because there are very few people who I can gather for a session of Warcraft 3, let alone ‘FroggieChat’.
The last thing that bothers me is that it leans hard into that ‘indie game’ aesthetic, which I am not a fan of to begin with.
It’s available for (Windows) Desktop and Android. Possibly more, I don’t care.
However, you have to pay for it, while all the other PictoChat clones you don’t have to pay for. A free demo is available which is local only and you’re limited to just three colors.^B)

Itch.io Link

Next to Pict.chat, which we’ll get to, this is the more faithful recreation of PictoChat. Evidenced by the fact it literally takes the UI from PictoChat. However, no Kana input, which is a shame.
This version is notable because it makes a number of improvements to the whole thing which are just nice. There’s a scrollbar, messages are automatically cropped and uh…that’s it.
This and the later one are both open source which I have mixed feelings on.
PaperChat is online rather than LAN, but you can create private rooms (or public rooms) so that’s an advantage over FroggieChat.
However…no keyboard support. That’s pretty weird and makes using it on desktop kinda pointless…which I guess is the…point? It also has an android app. I’d call this the definitive version of PictoChat that isn’t just PictoChat.

Website

This is probably the most faithful recreation of PictoChat because, unlike PaperChat, this one also includes Kana support. However…it does not include the improvements of PaperChat but, unlike PaperChat, this ones development is slightly more active and the keyboard actually works.
No Android app either, but it works on phones as well.
This one is online-only as well, but you can still create private rooms. If it takes the features of PaperChat, it will become the definitive version.

Website

All I’m getting from this is that I need to get to work on my own.