Trigger languages and something else

I'm working on one of my non-human languages, and trying to make its grammar
distinctly different from average natlangs.  In doing so, I've been reading
through some of the older posts and recently read some about trigger
languages.  If I understand it correctly, the system I'm using is kind of a
trigger language, but not like the ones you guys have been talking about.

In this language (Theodon), there is one word in every sentence that is the
"focus" or "topic" word.  (I'm not sure which term to use.)  All of the
other major words indicate what function the focus word has in the sentence.
Here's an example using English:

- The dog bites the man.
- Dog-focus bite-subject-verb man-subject-object.
- Dog-an bite-0-e man-0-en.
- Rhshroan thadshe géren.
/R\Sr\oan t_hadSe ge:r\en/

As you can see, "dog" is the focus of the sentence.  As it is the subject,
all of the other major words indicate this first.  (Subject-marking takes no
affix, so this is the simplest form.)  After taking an ending to indicate
what the focus is, the words take endings for their own function.  Here's a
different example:

- The dog bites the man.
(In response to, "What does the dog do to the man?".)
- Dog-verb-subject bite-focus man-verb-object.
- Dog-e-0 bite-an man-e-en.
- Rhshroe thadshan gérén.
/R\Sr\oe t_hadSan ge:r\e:n/

So here's what I'm wondering.  What is this sort of a system called?  Does
it exist in any natlangs?  Does it even make sense?

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