Even accepting your personal definition of "democracy" to mean "pure majority rule", constitutions typically have provisions for modifications by majority vote. So a being "bound by a constitution" does not eliminate majority rule.
So yes, it is a personal definition. Scholars don't use this definition. Pundits don't use this definition. The common man doesn't use this definition. It's a BS definition, and if it weren't, it would be pointless and redundant because "majority rule" captures this already.