If you include preserved seafood that is eaten uncooked, then raw fish and other seafood is moderately common in European cuisine. Restricting it to fresh rather than preserved seafood, there are fewer dishes, and seafood other than fish is more commonly eaten fresh and raw than fish. The two most common are perhaps oysters:
and sea urchin:
Herring is often eaten lightly marinated, not preserved:
and dishes such as gravlax and smoked salmon in their modern forms are essentially unpreserved. There are traditional dishes using cured/dried/salted fish, uncooked, such as the Catalan salad esqueixada:
and a variety of pickled and/or salted herring dishes in northern Europe.
However, as you noted, much European seafood is preserved/salted, and this is often cooked when eaten. Fresh raw seafood is largely restricted to where the seafood is caught/collected - traditionally, it was preserved (salted, smoked, dried, pickled, etc.) for transport away from the coast (freshwater seafood is less likely to be eaten raw, perhaps due to hard-learned experience with parasites). Fish being acceptable food for fast days created significant inland demand, and fish travelled. Feeding large urban populations also encouraged the preserving of food for transport. At least today, we often find a learned distaste for raw seafood (and meat) dishes apart from a small number of traditional dishes (e.g., oysters). Thus, it shouldn't be surprising to see few common raw fish dishes, and other raw seafood dishes.
How common is raw seafood in Eastern cultures? Traditionally, most fish and other seafood was eaten cooked, and much of it was dried, smoked, pickled, fermented, etc. There are some well-known raw seafood dishes, such as sashimi in Japan and hoe in Korea, and some raw seafood salads in SE Asia, but these constitute only a small minority of the seafood dishes. In some cases, these dishes are fashionable, and are probably more common today than they were in the past, outside fishing villages.
European cuisine is no stranger to raw meat dishes, either, especially if we include preserved meats (e.g., cured raw hams, fermented raw sausages). Fresh raw meat is still eaten today. Perhaps the most famous is steak tartare, but there are also broader traditions of seasoned minced raw meat in northern Europe (and elsewhere):
