I'm not sure I would consider Philidor a Romanticist. I'm not even sure I would agree with the definition. I don't think Romanticists were short on strategy. Of course, in the 19th century theory was still in its infancy, but strategy, even connecting the endgame to the opening, seemed to be relatively developed. Romanticists seemed to be more drawn to the open game since that type of game is more prone to yeilding combinations, and Romanticists considered combinations the highest and most beautiful aspect of chess. Speilmann was a Romanticist who was able to play in the higher levels during the first half of the 20th century, a feat that would seem impossible for someone lacking in strategical ability.
Steinitz, while he certainly took a scientific approach, started as a Romanticist - and was a good one. But as far as being the first truly scientific player, I don't know. He took many of his ideas from Paulsen who predated him in that style by several years.
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Nizamious did a recent articly on "the 10 greatest chess players" but I'm thinking about what people think about the 10 greatest ROMANTIC chess players. For those who are not familiar with the chess term "romantic," it refers to 18th century-ish style of play, which was more short-term tactics than long-term strategy. In my opinion the best romantic players were Paul Morphy, Francois-Andre Philidor and Adolph Anderssen. The first TRULY scientific player was probably Steinitz so he isn't included.