The building which was formerly the Hotel Europe (and, indeed, is still remembered as such) was designed by Parr and Fee for Angelo Calori and was constructed in 1908-09. It was, apparently, the third of Calori’s hotels. It isn’t clear where the first one was located, but the second hotel was (and still is) adjacent to (and remains an annex to) the flatiron block.
Parr and Fee clearly seem to have been influenced by Daniel Burnham’s Flatiron building (much taller than its 6-storey Vancouver cousin) in NYC (1902), shown below.
According to one source, whom I trust, Angelo Calori may also have owned the Princess Theatre (which in later years became the Lux Theatre and, more recently, a non-market housing block also called the Lux.
The Europe Hotel has been used as a set in various movies, including The Changeling (1980), Legends of the Fall (1994), and The Never Ending Story (1984).
Another early Vancouver flatiron block is here.