Skype works just fine on Android (I'm using it on a phone, but I don't see why should be any different on a tablet). Being the mobile OS, I don't think there is a distinction between a desktop or "universal" app. On my desktop (or laptop), I always use the desktop version of Skype, the universal (or modern or whatever) gets uninstalled right away. Perhaps, I'm not the only one with this usage habit and they are just going with the flow. Which is of course what they should do, rather than forcing something down my throat.
Once the web app starts, it tells me it needs to install a plugin, but when I went into Control Panel, Category, Uninstall, I found the Plugin has been installed, but I don't find anything else indicating Skype on my computer, except for Skype for Business 2015 in All Apps.