When the tool is already active, clicking the arrow enables the input field, also known as the calculator. This behavior is also present in other tools like Extrude. However, if you activate the tool and drag the arrow instead, the calculator will not appear.
I can see that on the first video, you have the “offset edge” tool activated. The 2nd video does not have this tool activated. Activating the offset edge tool and clicking on the arrow will activate the input field for the dimension.