"Being loaded ..." is a participle phrase. It adds extra meaning but it is not grammatically necessary (it is an adjunct in the sentence). It gives extra information about the guns, and in this case the phrase explains why these guns are not "empty relics".
The loaded guns contrast with the empty litter.
The style of writing is fairly serious and sophisticated. For example the structure of the first sentence has an interesting inversion (The meaning is "Eight guards walk by the litter", but the order has been changed to change the focus of the sentence in subtle ways)
You can make explanatory participle phrases fairly easily.
My car is slow, being nearly 20 years old.
My mother lives with me, having divorced my father.
The relevant section of the sentence:
... also relics of a more barbaric past but not empty ones, being loaded with pellets of soft iron
could instead have been worded as:
... also relics of a more barbaric past but not empty ones; they are loaded with pellets of soft iron
and the meaning would have been unchanged. "being loaded" simply means that the guns are loaded; this makes them "not empty". A previous sentence, if I recall the novel correctly, refers to another aspect of the parade (the king's litter I think) as an "empty relic. This wording connects this sentence back to that mention.
This simply a use of the present participle form ("being") of the verb to be. I am not aware of any special name for such a use.
For reference, this sentence is part of the opening scene of the novel, in chapter 1, and occurs on the second or third page in most editions, if I recall correctly.
