People tend to spend more per day in one's earlier trips than in later ones for a couple of reasons. First (or second!) time Europe visitors tend to be on the move a lot, trying to visit as many places as possible. All that train (bus, plane) travel adds up. On top of that, less seasoned travelers are more likely to be visiting the "must see" places, where hotel costs tend to be highest, whereas experienced travelers have moved on to other, cheaper places to visit. Admission to museums, castles, etc. are highest if you've never been to a place before and want to see the highlights than if you've been to all the "biggies" before and are seeing lesser (mostly cheaper) sights. Hotel expenses are generally higher for first time visitors to a city because it is usually preferable for them to stay in the parts of the city that are richest in "tourist target" sites, but where the hotel prices are unfortunately highest. For example, I've been to Paris quite a few times and I stay out in one of the outer arrondisements and save quite a bit. But if I were advising a first timer, I'd recommend staying much closer to the places (the Louvre, Notre Dame, the Eiffel Tower, the Seine boat tours, etc.) that I expect they will want to see so that they minimize time spent shuttling into the city from the outlying areas. Finally, when I visit a place I've been a lot, it's unlikely that I'll buy much in the way of souvenirs and mementoes, but a first-timer ought to budget in for that sort of thing.
I suspect that Rick's budget is geared more to the first or second time visitor than to those of us that travel in Europe a lot. And appropriately so, since that is the target audience of his books and this site.
I detect a whiff of smugness in some of our responses about how we beat Rick's projected budget that I think ignores some of the reality of first-time travel, and that I think may be off-putting to some, though I doubt it is intended that way.