Another key word is given in the third verse of the chapter.
For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and he will commend you. For he is God's servant to do you good. But if you do wrong, be afraid, for he does not bear the sword for nothing. He is God's servant, an agent of wrath to bring punishment on the wrongdoer (Rom 13:3,4).
The word usually translated as ruler is arkon. English translations of Romans always choose the strongest possible translation, but this Greek word can also be translated as judge or magistrate. It is translated as judge in Luke 12:38.
The context confirms that Paul is writing about submission to judges. The role of these authorities is to punish the wicked. This is something done by judges, not political leaders or military leaders.
We should also note that the word authority is plural. Paul is not talking about a single political leader. He is suggesting that we should submit to judges (plural). Romans 13 is not a message about a kings or parliaments, but a confirmation of the Old Testament teaching of the role of judges. There will be many judges and authorities and we must submit to the excellent ones.
This is consistent with the Old Testament, which always speaks of multiple judges (Ex 22:8,9; Deut 19:17,18; 25:1).