Well the 5 Days a Stranger series isn’t web-playable as far as I know, but in general yea I’d give those my highest recommendation for people looking to experience the old-school adventure style in newer games. The overall story is really well crafted. The first game takes place in present day, the sequel takes place like 400 years later, another of them takes place in-between, etc. Also one of them uses a text parser.
Two other phenomenal amateur adventure games are Pleurghburg: Dark Ages and Larry Vales 2 (play 1 first though). When I first played Larry Vales 2 a few years ago I got totally absorbed for a couple of hours, and when I finally took a breather I could have sworn I’d been playing a long-lost Police Quest or Leisure Suit Larry game.