Philologists study texts, definitely. The earliest philologists, in order
to study language change and language families, had to have ancient and
medieval texts available, so they took to editing texts and collecting stories
in unprecedented numbers. Their work was from the very beginning involved
in reading myths, epics, folktales -- they developed theories not only about
historical language change, but also about these older types of
literature. Those links you provided were very informative -- though I've
never taken a proper linguistics course, it was always my impression, as the
real linguists in your links point out, that linguists study language as a
system and particular languages (mainly modern). But they're not involved
in the study or editing of texts.
As for philology overlapping with other disciplines....yes, I would
agree. I'm still trying to puzzle out the situation at the beginning of
the 20th century, though, when different disciplines were becoming
established. On the one hand, I think it's right to say that philology
was too broad -- it overlapped with those other fields you mention, which went
on to define their boundaries and their methodologies more specifically.
Philology was too diffuse, maybe, to stand separately and on its own. On
the other hand, though, within English departments, philology came to be seen
as being too narrow in scope, as being incapable of providing a complete
approach to all of literature.
Today, you won't find job descriptions that call for philologists, but if you
were to consider yourself one, you would probably be someone who edits ancient
or medieval texts. That kind of work requires very broad knowledge: of
history, literature, language -- and very specialized knowledge: paleography,
codicology, different theories of textual editing. It's the specialized
knowledge that's hard to come by, because it is taught only by a few people,
usually in centers for medieval study or in literature departments if they
happen to have a professor who does that kind of work. But it's certainly
not part of the regular literature
curriculum.