If the goal of imperialism is to create an empire, why is the word not spelled "empirialism"?
Imperialism is first recorded in English in 1826, from imperial + ism.
The Online Etymology Dictionary says of imperial:
And for empire:
So both English words have roots in the Latin imperium (at one stage or another) and come to English via Old French where they spelled one with an E and one with an I.
Empire is essentially a French mutation of the Latin Imperium, which stems from the original Latin word Imperare which means "to command".