Valve describes their ideal employee as being "T" shaped, that is, comfortable and capable with many things, but with deep knowledge of 1 or more things. Even as a beginner, I think this shape is ideal, its just at a smaller scale.
However, there are other important things that a beginner must demonstrate that are taken for granted in more experienced folks.
Firstly, the ability to finish hard things. Most people can finish easy things, and most people can do 90% of a hard thing -- but you need to demonstrate that you're part of the 10% that can finish hard things, even when they're unfamiliar, confounding, obtuse, and just-plain-boring. Passion to solve problems plays a part here.
Secondly, the ability to learn and adapt. No self-study will prepare you for the unique environment and landscape of the teams you'll be joining. They'll all have historic cruft and unreproachable practices that just seem weird to outsiders, you need to be willing and able to fit in. You'll be learning knew things all the time. Passion to learn plays a part here.
Thirdly, the ability to communicate effectively. Its probably the single-most important soft-skill that we have. If you cannot understand other people, recognize and ask pertinent questions, or communicate your ideas effectively (usually, thoroughly and briefly) then you cannot be part of a team. Period. Full stop. Passion to share knowledge plays a part here.
Demonstrate that you can be counted on to do those three things well and consistently, learn at least a little about as many things as you come across (and learn how to leverage seemingly-unrelated skills/knowlege to perform better in each), and learn deeply about at least a few things that interest you.
Also, keep in mind that doing something very basic in one particular fashion (say, making asteroids in Unity and UE4), doesn't necessarily demonstrate much. It demonstrates a certain amount of adaptability and passion, and some level of learning. But it doesn't really say much about how much or well you know either Unity or UE4 -- to say you know either, you really have to put something together that exercises all of the moving parts at least, and preferably you've pushed yourself far enough that you've had to overcome real challenges in doing so. Then you can say that you're baseline-competent in one of them. You don't distinguish yourself or even learn all that much from doing what's easy, that only comes through doing what's hard.