You're starting from the wrong definition of mode
Etymologically, from the latin modus [as in the commonly-used modus operandi – method of operation, or working method.]
Etymological definition from Oxford Dictionary via Google
late Middle English (in the musical and grammatical senses): from Latin modus ‘measure’, from an Indo-European root shared by mete; compare with mood.
From the Cambridge Dictionary
mode (noun) WAY
a way of operating, living, or behaving:
- Each department in the company has its own mode of operation.
- Railways are an important mode of transport for the economy.
- Switch your phone to silent mode.
In user interface design, a mode is a distinct setting within a computer program or any physical machine interface, in which the same user input will produce perceived results different from those that it would in other settings.
Then from Wikipedia – Modal Window
In user interface design for computer applications, a modal window is a graphical control element subordinate to an application's main window.
A modal window creates a mode that disables the main window but keeps it visible, with the modal window as a child window in front of it. Users must interact with the modal window before they can return to the parent application. This avoids interrupting the workflow on the main window. Modal windows are sometimes called heavy windows or modal dialogs because they often display a dialog box.
So, in effect, a modal dialog changes the method/mode of operation/interaction with the application, as it must be completed/dismissed before you can return to the normal mode of operation. You cannot get ‘behind' a modal dialog to interact with the application as normal.