Little Princess (1986)

From the intro:

"It was a bright and sunny Sunday morning. I was on a date with my girlfriend, Miki. But disaster suddenly struck out of nowhere. The skies turned a foul shade of black. And out of nowhere, clad in the darkest of shadow, Dracula appeared to steal Miki away from me. I desperately pursued that wicked Dracula. And before I knew it, I was in a different world. Miki, I'll definitely save you. Please wait for me."

The game's story features the same Kentarou and Miki from the Rance titles, however Dracula would later be retconned and be replaced with Demon King Gi.