The Japanese manual states that you could get online and visit the game's web site: http://segaretro.org/images/8/83/MrDriller_DC_JP_Manual.pdf (scroll to page 24) I extracted the game's files and indeed, DreamPassport is there. But how in the heck I start the browser within the game? I tried every option without success.
It appears so - I just had a look at the manual you linked to, and the red box at the bottom of page 22 says this (probably a bad translation, since my Japanese sucks), but the meaning is fairly clear. "If you don't want to register with the Sega Provider (Isao Net) you cannot access the internet. If you are not registered, please carry out the registration using 'Dream Passport'. Also note that some old versions of Dream Passport do not contain the user registration function - in this event, please send a postcard to the network office requesting a copy of the latest version. Address: Sega Enterprises network office, 1-2-12 Haneda, Oota-ku, Tokyo-to. Postcode: 144-8531"
I was actually trying with emulators. Tried Nullcast, Demul, redream, reicast. Nullcast is the only one that in theory presents the modem to the game (I can see the logs in the console window), but looks like it does not save the registration information within the flash. I'll try in my Dreamcast instead.