There are unrelated. Besides downloading the Java app, you can play Minecraft in the browser through an applet at https://minecraft.net/play https://minecraft.

There are unrelated. Besides downloading the Java app, you can play Minecraft in the browser through an applet at https://minecraft.net/play https://minecraft.net/play. So no, if you are not running Java in the browser, a malicious web page can't run neither Minecraft nor other Java apps that you have locally installed.