I'm not so sure people view life as a game wrt having a "level playing field". They are looking at living the American Dream as a cutthroat endeavor where the competition wants to literally eat your lunch. While most of us are similar in mindset, that we seek to do well ourselves while hoping for others to likewise prosper, there are enough of those cutthroat people out there who would try to tear others down.

And that is where I see the concept of a level playing field coming in. Normal people just want an equal chance as everybody else. It is just a euphemism for equal opportunity.

The opposite of “level playing field” is the analogy “having a thumb on the scale”.
Whether it’s rigid class hierarchy, racism, or government intervention, it eliminates the goal of equal opportunity.