I wonder why “des” and “un” are omitted from the original sentence.

Because the sentence has the exact same meaning if omitted…

Not ommiting “de” and “un” here would be a sign of heaviness.

This is not the answer for your question, only what I know.

First of all, the sentence:

Je compte revendiquer mon héritage, des titres et un domaine compris.

is better expressed by

Je compte revendiquer mon héritage, y compris des titres et un domaine.

I intend to claim my inheritance, including titles and an estate.

The word compris when used as an adjective shouldn’t be used with words preceded by articles, be they definite or indefinite. This is also the case for the synonym inclus used as an adjective, so you won’t find

la taxe sur la valeur ajoutée incluse

You will only find

taxe sur la valeur ajoutée incluse

I am trying to back this up with some links but I failed to find any.
As to the why of that: I don’t know.

Second, as Stéphane mentioned in the comment (even if your comment indicates that you were after the first part)

Je compte revendiquer mon héritage, titres et domaine compris.

would be equivalent to

Je compte revendiquer mon héritage, y compris les titres et le domaine.

I intend to claim my inheritance, including the titles and the estate.

not to

Je compte revendiquer mon héritage, y compris des titres et un domaine.

because there’s this assumption in the first sentence that the titles and estate are known.