Ahh. Semantics. Fun
It was more to use the figure of speach correctly. Some people see no need to draw a difference between "games" of skill and "games" of chance. Colloquially they are just all called games. But thats not historically how the US legal system has defined it. Without some notion or requirment of skill, those games have not been classified as "games", but as gambling systems. The US government has a long history of frowning upon any sort of gambling that isn't State sanctioned, and the history of Pinball machines being outlawed in this country between 1940 and the mid 1970s is a prime example.
If Chutes and Ladders is a game, then flipping a coin is a game. Neither take into account skill on any level. 100% chance. I do not know if I would ever consider coin flipping a "game" personally.
Solitaire and War have some semblence or notion of skill. You can certainly play your solitaire cards incorrectly and lose because of it. Same with War.
Competition is interesting. I disagree slightly, but there is no competition without a skill element present to compete over.
If Chutes and Ladders is a game, then flipping a coin is a game.
Of course it's a game. If I want to flip a coin over and over to see how many heads in a row I get, that's a game. A game is anything you do for fun. If someone feels their games have to include a skill component to be fun, that's perfectly fine, but it doesn't invalidate every other kind of game in the world.
I'm actually not familiar with War, but according to its Wikipedia article, whether it's a game of skill or chance depends on what rules you're using. If you can choose the order that cards from a war are put back on the bottom of your deck, there is a skill element in deciding what order you want them in. If the order is preserved unchanged from when they were revealed, the only skill is memorization and card-counting. And if they're shuffled before being put back, the game is completely random and skill-less.
Very fun!
Honestly, I wouldn't even rate Sentinels as my favorite game. Top 5 for sure, but BattleCon at least trumps it.