I have always understood that higher compression ratios in a gasoline
engine were one of the approaches to get higher HP, yes. Interestingly
enough, turbo charged gas engines are often set up with lower
compression ratios than their NA counterparts- but due to the tubo
boost can still provide more power.

I agree that it might have been more accurate to say that gasoline
engines rely on spark, rather than "require" spark for combustion. If
one were to inject gasoline into a cylinder compressed as much as air
is compressed in a diesel cylinder, it's my impression that it would
ignite very easily without a spark. Too easily, in fact.