[..] The best way I've found out to make it work properly with a MSX was to have a custom firmware made for it using Arduino IDE with ESP8266 support.
Yes, Arduino firmware can do the trick. However, I use NodeMCU firmware. This allows me to update new versions of the lua-code to the esp via wifi and NodeMCU allows easy event-driven programming. I have now a simple HTTP-server, a telnet server and a UDP "server" running simultaneously on the ESP (each in different Lua-scripts, optionally triggered during startup) as well as a serial-server to communicate with the MSX.
The HTTP server is used to configure wifi remotely via "http name_of_esp/config.html", and store the config on the flash of the ESP. The telnet server is used to transfer Lua-code to the ESP (and this can also be used to upload new wifi.cfg, which is a simple textfile).
Apart from the getip.com and getmask.com I have yet to add more commands to make it more useful (but that is just a matter of time 
)
If you aren't seeking UNAPI compatibility and intend to create programs seems fine, I've started SM-X network driver like this and soon realized that UNAPI was the way to go as it has lots of tools and programs already working for it. 
It is great to see old hardware being rejuvenated to get cool new functionality 
You may be right: UNAPI might be a next step. For now it seems overkill to me (excuse my French ;-) ) as my poor-man's wifi interface requires the MSX only to send some commands to the ESP where the ESP is doing all the work and sends results back to the MSX...
... and imho there aren't that many useful commands in MSX-DOS for this old MSX system (albeit a wonderful system ;-) ).
- get or set ip, mask, wifi-stuff
- get_dns "hostname"
- get "file" from "host" (via FTP or HTTP) and save or execute
- post "file" to "host" (via FTP or HTTP)
- telnet "hostname"
And what these commands do exactly is defined in the ESP, where the heavy stuff will be done.
... hmmm, I can imagine some multiplayer MSX RPG game via Internet 
Update: I have now working:
- getip
- getmask
- whois
See example screenshot:
... maybe in the future someone can help me with UNAPI?
