That timescale was for our first design, which was scrapped (our Kirby if you like, although still on the same site).
After that was scrapped we went on a wild goose chase to try to win the Olympic Stadium site, which (thankfully) failed. The first we heard of the new White Hart Lane stadium project being back on was in 2012/3 iirc.
The new design for that was revealed in July 2015, planning permission gained in December with the build starting more or less this year (I say more or less as the basement was a separate planning app). But that was a quick approval because a lot of the issues had already been ironed out with the first (scrapped) scheme. We already had permission for a big new stadium on that site, so a change in design and relatively small increase in capacity from the first scheme wasn't the biggest hurdle to overcome.
You're completely right to say this is a long process though. People expecting timescales of weeks rather than months or even years need to realise that! It seems to me Moshiri hired an architect almost as soon as he became properly involved in the club. It looks like things are moving quickly to me. Not that that means it's a definite goer, but patience is required.