No! You should see on right side of the open file tabs 2 small arrows to scroll the tabs left/right.
You can also increase the height for the docked file tabs. In this case UltraEdit will automatically arrange the open file tabs in multiple rows. If you move the mouse over the lower border line of the file tabs, the mouse pointer will change into an up/down arrow indicating that you now can left click on the border line and move the border line down while holding the left mouse button to increase the height.
You could also undock the open file tabs view and resize the window to whatever size need to show all file tabs at the same time. Undocking the open file tab can be done by double clicking on the left border below the small x symbol. To later dock the view back, double click on the title bar of the open file tabs bar where "Open Files" is shown.
Best regards from Austria