You don't install Java, you just unpack it from
a zip file like this one.
In case you missed it, the GitHub project with pre-built Windows OpenJDK Java 8 binaries is right HERE
Please do your self a favor and use a proper open source OpenJDK build instead of ..., ah, never mind.
Java 101 for a curious Blood/BloodGDX fan
You see, there is no single version of Java. Multiple vendors have their own branded "Java versions". Oracle has one, IBM has one, Azul systems has one etc.
For some unknown reason, people land at Oracle and think they need to install Oracle Java, which installs a boatload of stuff you don't need. The truth is, you don't need Oracle Java to run BloodGDX.
There is this thing called OpenJDK, a.k.a RI (Java Reference Implementation) which is under GPL and open source. It works like this: Java is developed in open but the companies funding the development brand it with their stuff and bundle it with their products before it could reach customers. So, in essence, all you need to do is to get hold of the not-yet-branded reference Java implementation a.k.a OpenJDK and either build it your self or get pre-built binaries for your platform and voilà you have installer-less vendor-less Java... end of story.
And yes, BloodGDX works with OpenJDK just fine. I know because I play it that way, on Linux.
DISCLAIMER: I have no Windows. Somebody with that operating system should take the above OpenJDK build for a ride.