As someone who has a basic understanding of Java(purely on the client side, haven't done anything with NodeJS), should I continue with refining my knowledge in ES5, or just jump straight into ES6? This site looks really neat, I should add.
Java != JavaScript. While offering some cool new things, ES6 is overall a fairly incremental change. I would concern myself with learning the fundamentals of the language first.
Just wait until Java starts compiling to WebAssembly and skip learning JavaScript altogether.