In case of Industrial, Modern and Atomic eras you are certainly right, though Japan has been spectacular exception.
During renaissance era (I hate this naming, it really should be "early modern era", we're talking about approx 1492 - 1789) I'd argue that Europe was steadily increasing its initially small tech and economic advantages but it was not yet
that much stronger than rest of the world. Only since the 18th century Europe was capable of truly curb stomping Ottomans and South Asian polities on the battlefield, up to this point there were several civilizations capable of fighting it 1:1. Also, before the industrial revolution Europe still didn't have
that crushing advantage in economic terms - Pommeranz argued in his famous book that until the late 18th century the most developed areas of China were very comparable to the most developed European countries in "proto-industrial" and "proto-capitalist" terms.
However it is also worth noting that in game terms "4 out of 8 eras" means IRL "500 years out of 6000

(200 years and 3 out of 8 eras in the alternate narrative). I have never liked how heavily Civ era system is biased towards more recent history, I would seriously argue for "early medieval" era just to prolong pre-modern history.