Survival games existed before Minecraft but in a very different form.

Survival Kids is a konami series of games that started on the GBC and went on to have 3 more episodes on the DS, where the premise is always “you’re stranded on an island and must find a way to be rescued”, but unlike modern survival games, the world is custom built and the evolution of the plot is usually pre-determined, with maybe some branching but nothing extremely dynamic. You also couldn’t alter the game world in any significant way beyond what was already expected, such as building bridges in predetermined spaces and so on.

It has some hallmarks of the later versions of the genre, like an emphasis on crafting and needs management such as hunger and thirst, so the connection is definitely there.