The difference between logged in and logged out looks to be cached CSS. Clearing or disabling those caches should fix that.
But overall, there still isn’t enough room for all the menu items to fit in a single row on smaller screen sizes, and as the screen width reduces more menu items are pushed to the next line.
To stop that happening on any size screen would mean reducing the width of the menu items, either by trimming text, reducing font sizes or menu item spaces… and then if need be breaking to the mobile menu on a larger screen.
All of which is possible, but perhaps not what you want. Let me know. Or if theres an alternatove