From loosely following chess over the past year it seems they normally play a random pool and whoever has the best score at the end wins the tournament.
No that isn't the case. There are really only two common types of tournaments. A round-robin will see each player play every other player once but this is limited to small fields (10 is the usual limit).
For big fields like the one the article is about the Swiss System is used. Each player gets 1 for a win, half a point for a draw and zero for a loss. Players are mostly paired against those who are on the same score each round. I say "mostly" since there are all sorts of rules to decide the exact pairings. Chess tournaments will use Dutch-Swiss or sometimes Dubov-Swiss