You make a false equivalency between gaming and escapism.
You're right. Gaming is just like any other entertainment and there's nothing inherently wrong about entertainment, as long as it doesn't take up disproportional amount of one's attention. Almost any pleasure-inducing activity can turn into escapism if one uses it as a constant distraction from the hardships and responsibilities of daily life.
But even if you hadn't, "escapism" is not unequivocally bad. No matter how much stock you put in the philosophy of "power" there is going to be shit in life you are powerless to affect. Your wife dies in a car crash, you're drafted to war, whatever the case, finding respite in another world, in whatever medium, is not a "distraction from the truly meaningful activities of life." Gaming or reading or music can serve as distractions from immutable, invariable negative external forces so that you can do the things you have to do in order to flourish as a human. They can also provide perspective to process grief, tragedy, or whatever else.
This is where I disagree with you. First of all, I define power a bit differently from Nietzsche, who was obsessed with individual, tyrannic power. To me power is simply all those resources we have that let us influence out internal and external reality. Our health, bodily functions, all of our senses, our relationships and the benefits we enjoy as members of various collectives all add to our individual power. You might want to read the forum link thread I posted before if you want to argue this definition further, since the topic is discussed there in length. I leave the link here just in case you want take a closer look.
http://onlinephilosophyclub.com/forums/viewtopic.php?f=1&t=15226
Now, to me it's obvious that we encounter events are realities in life that we're powerless to change or overcome. Let's take your example - your loved one dies in a car accident. I lost by brother in a car accident when I was young, so I can relate well to this example. This kind of loss unavoidably creates sadness and it can immobilize and incapacitate us even for a long period. However, from the perspective of individual's well-being, one of the worst responses to this kind of event is playing video games 24/7 to numb the pain away. By sweeping negative experiences under a rug will only make the eventual recovery more difficult. Instead, a tragedy can be a transformative experience - you can become more goal-oriented and determined by reflecting on how short and fragile a life can be.
How you deal with negative external forces? By enduring them, by facing them head-on and not letting them discourage or distract you from doing what you should be doing. Train your mind and body to withstand hardship. This is where I agree with Nietzsche.
Games, books, and music can resonate with people intellectually and emotionally, they can challenge (e.g. playing chess with a skilled opponent), and so on, and there are certainly ways to incorporate the associated hobbies into a "truly meaningful" life.
Certain type of entertainment can be useful, yes. The problems arise when entertainment becomes a bad habit, which they often do. Good habits are difficult to gain, but easy to live with. Bad habits are easy to gain, but hard to live with. Unfortunately gaming in most of it forms fall to the later category - it becomes a time-consuming distraction that doesn't aid us to become the best version of ourselves. Like I said before, all decisions about how we spent our time are value judgments. Adopting a habit of exercising instead of playing games is surely more advantageous for one's health and well-being. To me true happiness comes from power acquisition (remember the definition I mentioned above). A constructive habit like exercising leads to more power acquisition than gaming, and is therefore a more preferable use of one's time. Therefore we can conclude that gaming, for the most part, is a waste of one's time. In other words, if one decides to incorporate gaming into his/her daily habits, it will not be the best use of his/her limited time.
If you have not already, I recommend you study Spinoza's Ethics and Aristotle's Politics rather than Nietzsche. Iconoclasts and übermenschen are not stable models for human excellence, and the Conatus doctrine is much more concise and well argued than Neitzschean "power-centers" or his resulting theory.
As I mentioned above, my definition of power differs from Nietzsche's. I'm actually not really interested in metaphysics or abstract approaches to ethics. I appreciate the concept of power (as defined on the forum thread I linked above) because it works in practice. It is directly applicable to our everyday life, instead of simply being a vague theory about how the world might be or how it ought to be.
I believe I mentioned Spinoza briefly on the thread with regards to how Nietzsche referenced him. I don't actually think Aristotle's or Spinoza's views on a meaningful life are in sharp contrast to how I define it - I merely take a slightly different angle to it. Strifing towards everything noble and good as defined by society is very important in terms of power acquisition. Knowledge is power, so strifing to gain more knowledge is essential part of power acquisition. To me Spinoza's philosophy is however far too focused on rationalistic theorizing and loses touch to practical realities of everyday life. Although I have the highest admiration towards Aristotle, he is a bit far removed from contemporary life to be a very practical guide to how contemporary people should live their lives. All I'm interested are practical contemporary approaches to obtaining a meaningful life.