Does culture comprise political institutions and system of ruling?

Question

Since culture comprises everything that is the product of human efforts.

Answer 1

It would include them, as your second line implies.  But culture also includes the natural world which often has a strong influence on economy, religion, borders, sports and games and pastimes, and so on.

Answer 2

The political institutions do not look upon themselves as cultural.

They are the rulers, giving the laws, judging and leading in correspondence with thees laws.

Cultural institutions deal with art, literature, theatre, song, etc.

This is my point of view.