It's a good thing to look at relationships and coupling as a "game" because too often we treat finding our partner as a "fairy tale" story where it's just a matter of "meeting the right person". That myth does a disservice to everyone: both the couples who find someone but then need to work on the relationship, and the people who have unrealistic expectations and end up alone.
Also, even if it doesn't inform individual choices, it's useful for looking at things in terms of broad demographic trends. If the article is right, it means there's a potential demographic shift coming of fewer children, fewer people with supporting family structure, etc. Understanding the dynamics behind that can be important for planning a society's future.
Maybe it's because i don't understand dating as a competitive activity and my social interactions are very limited that i don't understand where are decisions to make (a.k.a, how people "play")
Yes, this seems to be the case.
And I don't say that to put you down - I actually used to be the same way. As a highly analytical person working in the engineering field, I used to approach dating as a rational activity. You know, you meet someone, and if the two of you are compatible then you start a relationship. Or at least that's how I thought things should work.
As I got older though, I realized things could not be further from the truth. Dating is an activity that is driven by two things: biological imperative of the two genders (that are different) and the emotions that are governed by those imperatives.
Once I understood that - i.e. once I accepted the politically incorrect fact that we are mammals first and foremost - everything started making a lot more sense.
Now, the way you guide your own dating life, should, presumably, be done in a way that is good for you and not harmful to others, but this is more of a Golden Rule thing rather than a game theory thing.
Don't get fixated with the 'game' word which has a loaded meaning outside of game theory, it's just a math term here.