When I think of 1-player games, I think of sports like running, bowling, swimming, and golf. The soul characteristic that differentiates most 1-player games from multi-player games is that you are only competing with your best self. If a swimmer swam the world record in practice, they know that they are capable, and the challenge becomes replicating that experience whenever they want to (ie during a competition). A lot of unofficial world records have been broken during practice. When we considering having to replicate an event, we are challenged to understanding why and how we did so well. Understanding the 'why' and 'how' differentiates the greats from the luckies.
Multi-player games are a lot more dynamic because there are so many moving parts. There is no turn taking; I play as you play. Because of this some would say that multi-player games are closer reflection of the world than a 1-player game. In multi-player games, you can capitalize off of other people's weaknesses and mistakes as opposed to building your strengths and personal definition of success. In a multi-player game, someone can win because of someone else's unforced error instead of winning because they performed to the best of their ability that day.
Does a swimmer watch video of another swimmer or do they just swim? Does Tiger Woods study other golfers at all or does he just practice on his game? If I was a golfer today, I wouldn't compare myself to Tiger Woods; I would compare myself to me (so that I don't get discouraged). As much as I would like to win, I would focus on beating my personal best score. If his best is a 10 under par and mine is a 4 and I shoot a 6, then I've beaten my best self though it may not have been better than Tiger Woods' personal best.
When we think we're playing other people, it's extremely easy to externalize loss (ie The referee cheated. He had a head start.) and take credit for victory (ie We were just the better team). At the end of the day, whether 1-player or multi-player, all we can do is our best. If we truly hone in on our unique purpose and define what we want to be and were created to be #1 at in the world, no one can or will compete with us and the competition will only be between us and our best selves. We need to let go of the underdog mentality and start thinking like champs; underdogs don't think like underdogs. We are our best coach and competitor, so we need to stop playing ourselves, and really...play ourselves. We define the game by how great we want to be, not by other people.
What if we study ourselves too much, pulling us out of this unification, and studying ourselves singularly constantly, it makes things awkward often