Thanks for the question.
Mattermost runs in mobile browsers and you can create a shortcut key to make it a mobile web app--and we'd probably accept a pull request to the Mattermost Push Notification Service to send HTML5 mobile notifications.
The current Mattermost native apps use a hybrid approach, rendering the Mattermost mobile web experience inside the app, while supporting push notifications via native iOS and Google Play infrastructure.
There's React Native mobile apps being developed as well.