Welcome back, the game is much better than 15 years ago! Yes you can download the web app as a standalone app at https://mysterious-castle.com/, just press the "Play in your browser" button and follow the instructions to download a local copy that looks and acts like a normal desktop app. I have tested on Chrome, but it should work with any modern browser. Otherwise, I would suggest playing on your phone or iPad, the game was always designed with touch interface in mind, although it plays pretty well with the mouse too.
Hope you have fun!