To download the app as a mobile web app, click EXPORT > HTML/JS/CSS:

Publishing Ionic app as HTML Website

Here are the simple steps you can take to publish your Ionic app as an HTML website:

Download the project and unzip it.
The folder should contain package.json.
From inside this catalog, start npm install (you need to have node.js and npm installed): all the dependencies will need to be installed from package.json.
ionic serve will start the project preview.
ionic build --prod will create the project build that can be then uploaded to whenever you need it.

You can also check here for more details.