In, for example, a terminal window, if you double-click (select word) or
triple-click (select line), and then drag, the selection is from the
beginning of the word/line to the current mouse position.

In GtkHTML, however, even though when you double- or triple-click it does
select the word or line, if you then drag the mouse, the selection becomes
from the original click point to the current mouse position, rather than
from the beginning of the word or line to the current mouse position (as if
you had only single-clicked).