Interesting debate. I always play to win - the number of times I've got into arguments with the wife because I've come late for my dinner as a result of having to finish a game is a lot! But I absolutely cannot just give up, I think the house would have to be on fire for me to leave an unfinished game, although I do sometimes give up when its clearly a lose cause - I'm not one of these people who fights to the last piece when there is clearly no chance. But as long as I still think I can win, I play on. Against top players, this requires a lot of concentration and effort, and the game is normally at least 30 minutes long. On Gravon this is one of the advantages of being able to pick and choose who you play - if you are tired and don't fancy toughing it out you can look for a lower ranked opponent and likely an easier game. These are the times you just want to play for fun.
So you ask, if you aren't playing for fun, why play the best? And the answer is because the fun comes in winning those games! It's an enormous buzz to win a hard fought game against a world class player, its exhilarating in fact. When you have the time and the energy and you settle in to take on a juicy opponent, you have to have the right mind set and if you have that, and you are a decent enough player, you know you have a chance to win. If your mindset isn't right there really isn't any point playing the game. This is where on this site I opt for a quick game instead because that's just a bit of fun with no consequences.
Not everyone wants to turn their stratego into something that meaningful, not everyone is competitive enough to care about their rank or if they win or lose. Those people rarely become very good, let alone among the very best and that is the same in any discipline.
To conclude, there will now be some people going 'ok but then what's the point in taking it so seriously and putting so much into it? Its just a game!' and I think the answer is each person gets out from it what they want to get. For me the fact there is no audience, no prize money, no trophies - doesn't matter. I get an enormous sense of satisfaction from winning and this is something I win a lot at. The pinnacle may come in beating a top player yes, but I still very much enjoy beating players ranked below me. I can beat a silver player and get only 1 or 2 points for it but the win is what counts, not the points.