There are several pieces of software in the Solus repository currently that play midis out-of-the-box. Just install MuseScore. It comes prebuilt with a soundfont. Load a midi, play. Another perhaps superior option if you wish to play and edit midi is SunVox.
Remember, midi isn't an audio format; it's audio instruction language to be interpreted by a computer that then assigns a soundfont's digital instrument samples to play it. On Windows for many years way back in the 90s and early 2000s, they'd package up loads of audio software to contain soundfonts and do all this under the hood, giving the appearance that midi is analogous to mp3 or ogg, etc. On Linux and in general nowadays, audio players typically don't come with midi support. I suggest you give SunVox a try. If the package still cannot be installed due to the migration, download SunVox from the SunVox site directly -- it's just a right-click -> properties -> 'allow app to run' deal, and it works great on Solus with absolutely no configuration, easy colorful interface. This way, you can play your midis, then export them as mp3s or whatever format you wish for your audio playing convenience on any player. Good luck.
[EDIT] lol Somehow I completely missed the content and contex of the original post and only comprehended the thread title. Yeah, getting OpenTTD to play midi is going to be a somewhat more complex problem, unless the game itself is compatible with other audio formats and you could convert the midis and drop in the replacements. Seems not, though. Basically, it looks like the Linux version relies on TiMidity++ to automatically play music in-game. I guess that'll have to be added to the repos. Till then, you'd have to compile it yourself or tell OpenTTC to use fluidsynth, as you already figured out. Maybe check the Arch wiki OpenTTC page for this and other solutions. This isn't a Solus specific problem, apart from the current lack of Timidity in the repos.