Nice video. When I was very young, my family and I went on holiday to the same hotel in Spain a few times, and the hotel had Sega Rally 2, The House of the Dead III and Snow Bros. units in its arcade that I played the hell out of in the evenings.
I didn't play Sega Rally 2 for years and years afterwards, until I got a Dreamcast for my birthday last year. I included Sega Rally 2 in my initial batch of games simply to have something that I could play splitscreen, and yet it wound up becoming my most played, and debatable favourite, game on the system.
Side by side, the graphics of the Dreamcast version are a definite downgrade compared to the arcade original, though I was surprised not to notice the difference too much when I found an arcade unit in the wild last autumn, and the Dreamcast version is still visually respectable for a launch title on the system. The framerate is a little uneven at times, though I only really noticed it in multiplayer, where it unfortunately inteferes with the experience.
You hit the nail on the head though in saying that the Dreamcast version maintains the same fun as the arcade original - drifting through these lovely landscapes so freely brings with it a real sense of joy and exhiliration that most racing games strive for. I would also say that with a proper racing wheel (i.e. an MC2 or a modded Race Controller/Rally Wheel), this game becomes even more enjoyable.
I also don't think the extra features of the Dreamcast version get enough attention - they could have very easily put out a fairly direct port of the arcade version à la the original Sega Rally on the Saturn (which probably would have made the port's shortcomings stand out even more), but the drastically expanded range of tracks and cars over the arcade, plus the 10 year championship mode, really give it staying power.
I guess the one real bummer I have is that not only did the online multiplayer mode never make it out of Japan, but it's also apparently quite unlikely that it will ever be revived, thanks to the tech behind how it worked. Never say never though...