It’s distinctly not pirate king though. Pirate King refers to the person who finds Raftel, showing how they conquered the seas.
Doffy had no interest in finding Raftel. He wanted supreme power, or rather, the power he believes to be his denied birthright.
The supreme executives are tools, even Law thinks they are nothing more than Doffy’s clownish puppets.
While they are closer to Doffy than most people, someone like Trebol is projecting a great deal of his own desires on Doffy.
That´s one interpretation. You are missing the point of reaching Raftel and what it implies.
People were talking about Roger ruling/conquering the sea like a king, hence the title Pirate King was born, that title did not exist in the first place, we saw that in the flashback (so obviously Xebec was not aiming for that). That´s why Rayleigh asks Luffy is he actually can conquer everything in Shabondy, it´s implied in the title, everything is below you and belongs to you.
If someone is ruling the seas without any doubt, but has not reached Raftel, nobody is going to say "but he did not reach Raftel, can´t be Pirate King", that´s nonsense. Croc is the prime example, had dream of becoming PK traditional way, got crushed, looked for different ways to acquire power to reach his goal, namely Pluton.
Whatever Law says is irrelevant, he has a subjective viewpoint. There are scenes in context with Doflamingo, and for example, Vergo, that clearly underline that they are not merely tools, they are still his family but he is ready to sacrifice them as he did his blood family as well, because his goal has bigger priority. And Vergo for example knew that, and still treated him like the king regardless. Same for Monet, they were not blindly sacrificing themselves because they had illusions that did not exist, they are a group that got together because of DD and is held together by DD, and the members see his success as the main priority (which is an obvious parallel to the Strawhats and Luffy, especially with the timeskip).
A scene like this would not happen if all they were were tools, because Vergo was not useful anymore, so there is no need to pretend, it´s really to express his gratitude and his love, even calling him partner.
And here you see Doflamingo feeling misery due to the sacrifice
To me it seems like a lot of things regarding DD went over people´s heads, or they were buying into disconnected statements rather than look at the entire picture with everything Oda has implied.
Doflamingo, by far, was the most complex (for OP standards huge) antagonist the series has had so far, and he had notions which to some people might seem contradictory, for example loving his family but still sacrificing them.