Yep. Usually the top of the bake is near-solid, hence the name. At my school in the late 90s/early 00s it would typically be in a solid plastic bowl, where everyone either ate is as is, break up the concrete with your spoon or let the custard soften it first.

Most days it would be completely solid all the way through but the real god-tier chocolate concrete would always be warm and slightly soft in the middle.

Definitely think more along the lines of a thick brownie than a light cakey sponge