I think, the searchbar is to big and/or the text of your buttons is to long. there is not enough place.
maybe, in the style properties you can find an option to change it to an icon when the screen is lower than size xxx
I'm not to sure I could be wrong but I think that's where the responsive options come in to play maybe @Russ or @Steve can shed some light on this. I do know when I turned the responsive options off on my site it was nearly impossible to navigate on my iPhone 7+ my advice in these times more people are using tablets and phones to go online I would keep it as mobile friendly as possible for members.
It is the responsive option being disabled. The default responsive navigation doesn't kick in for XenForo so the links aren't collapsing into the ... menu. It needs to be disabled, if you're trying to just make it like a "desktop" version of the site, re-enable Responsive mode and add a min-width: 1000px; or whatever value to: Style Properties -> General -> Body.