The two examples you gave don't prove your point. If you want to play those games at a high level, you need a good account with access to the good game pieces. Technically, you can acquire those pieces entirely for free by investing lots of time into the games (something that's entirely impossible with paper M:tG). This is literally the same as saying "to play high level Magic you need to have a good deck, but that's just the cost of playing the game".
If Magic =/= pay-to-win then neither do those 2 specific examples you just gave.
I don't believe there is a competitive (read: >2 players) game that is "pay-to-win" if you feel that magic isn't pay-to-win
At least the last time I checked, most Clash Royale and Clash of Clans players don't play with the best game pieces, because too much grinding or money is required for it to be worthwhile. In contrast, a much larger fraction of M:tG players (though still small in absolute terms) play with all the game pieces they want, and are only idea- and skill-limited.
Yes, in some sense the difference between M:tG's "~$50-500 for the best game pieces, or to enter major Limited tourneys where everyone is forced to start from scratch, for a year; only skill matters from there" and Clash Royale's "~$5000, or an amount of time and attention worth >$5000, for the best game pieces, otherwise you're strictly behind someone with higher-level versions of your pieces" is only one of degree. But again, a far larger fraction of M:tG games involve both players playing with what they consider the best pieces. I don't believe I'm the only one who sees this as amounting in practice to a difference in kind.
If Magic =/= pay-to-win then neither do those 2 specific examples you just gave.
I don't believe there is a competitive (read: >2 players) game that is "pay-to-win" if you feel that magic isn't pay-to-win