To be able to vote in Dutch national elections, as a Dutch citizen living abroad I need to register with the municipality of the Hague. Does this make me technically a resident of the Hague?
No, you are not a resident of The Hague if you live abroad.
Note that you are only able to vote in national and EU¹ elections. You are not able to vote in next weeks municipal elections.
All adult residents of The Hague are able to vote in The Hague's municipal elections. As you are not able to vote in the municipal elections, this logically means you are not a resident.
¹If you live in another EU country, you can choose in which country to participate in the elections.