Shooters are popular because of making for the most dynamic-yet-complex PVP experience - they're perfect for multiplayer gaming, and, well, multiplayer gaming is thriving nowadays
Minecraft is popular because of its universal appeal - kids can play it because there's no sex or violence, adults can enjoy it because it's complex; slow-paced players can dig into building and farming, fast-paced players can explore dungeons and smack everything with a sword; casual players can get deep into exploration, hardcore players can try and make all sorts of crazy stuff (like computers or space shuttles); etc, etc. There's just something for everyone, and that broad range makes it so popular. The only thing that baffled me at first is how it's popular around children, but that makes sense too in context - again, no blood and gore, and aside of Oregon Trail, it's probably the closest to make you learn stuff (especially when it comes to redstone - some heavy logic involved) while actually being entertaining. I'm kinda happy so many kids prefer stuff like Minecraft and Terraria, rather than CoD and GTA (like it was a decade ago).