You are using a faulty definition of vegetarian. What constitutes meat has nothing to do with what constitutes vegetarian. Think vegetarian == non-animals (or animal kingdom) or better still think vegetarian == vegetable (vegetable kingdom). I'm a long term vegetarian (>14 years now) and I hate it when you go into an eating place and ask about vegetarian dishes and they list the fish and chicken dishes because some-one who doesn't eat whatever (usually "red" down here) meat (for whatever valid reason) and calls themselves vegetarian.
For the record I've never had a tofu cheesecake but I'm not against trying some if some-one is offering :-)
Do not seek to follow in the footsteps of the wise. Seek what they sought. -Basho