It should be possible to create a subset of the popular bootstrap classes used in Moodle content and add them to the app so that your example "just works" as it is. I think it could be done via the same mechanism that lets you change the colours of the app by providing a link to a CSS
file so someone could work on this without needing to convince the mobile app developers it was a good idea.
It is.a reasonable amount of development though, and it seems no-one has done that up front work yet to make this possible.
Complications include the fact that the mobile framework has seperate styles for different platforms, and the mobile app is transitioning between two versions, though you can provide different styles for each version. So making it all work seamlessly for all platforms and all possible bootstrap classes is a big job.
But incremental progress is possible. So just copying and pasting the standard Bootstrap CSS for .btn and .btn-default into a CSS file somewhere and pointing the mobile app to it in settings would at least make these links "button-y" and people could build from there to make them more native looking or add other popular classes like badges or alerts.