Does this mean that I cant just simply copy the private key from this .dat wallet and import it to electrum? ... and after that just start transfering bitcoin as I usually would using the bitcoin core app?
Master private/public key: no, because Electrum wont be able to derive the hardened addresses of Bitcoin Core, it'll produce a different set of addresses.
Private key: yes you can, because the address can be derived from it.
The downside is, it's for a single address so you either have to know which key to export or export all of the wallet's private keys.