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A tournament is a tournament, but I think the discussion is too focused on them! And what if there are only 2 participants in the tournament? How will it differ from a regular match? And how will it differ from a large tournament, for example, with 16 players? That's the point: it's like a proportion. Only the values are different: the second one is naturally better than the first.
But both are still tournaments. I think that each match should be considered separately, based on the fact that only 2 participants compete. And then calculate each match separately. Besides, calculating the "coolness" of the participants is an extremely unrewarding and unnecessary task. But many do not agree with this.
The importance of the tournament. A separate mini-formula could be created: each place is given a bonus depending on the place taken. Although I am leaning towards a simple number. Starting Player Rating: 0. Because, in theory, it should only increase. Otherwise, a player with no games will always have 100. And another active, but losing player will have a lower rating. This is unfair.