But it shouldn't be a surprise that there were tournament events organised prior to 1851. While not attracting the stellar field of the London event, they would certainly match the definition of a tournament, at least in a rough sense.
The earliest such tournament I could find was held in London in 1788. While mainly consisting of English players, the star attraction, and event winner, was Philidor. The tournament records (from Chessbase) show that he played in the vast majority of games, so I wonder if it was a series of short matches involving Philidor, with a few side games between the other participants.
From this event I have chosen one such side game, between Bowdler and Conway. It is a game of that time, as Bowdler disregards material to focus on a mating attack, while Conway obliges by taking everything, and getting mated.
Bowdler,D - Conway,M [C23]
London London, 1788