The input fields on the screenshot and the ones on the link look different. The one in the screenshot seem to have the mw-ui-input class applied.
The issue is happening because VForm adds the mw-ui-big class on the submit form. The text fits properly once its removed.
Another option is to not use VForm and build a normal HTMLForm. But that would make it way too wide.
I think the best option would be to setId on the HTMLForm and set the width from a CSS within the extension.
(Argh, that screenshot is actually misleading, I've only now noticed that the text of the message has been changed. But either way, the new button will just get wider to accommodate the text.)