Yes, you could consider Dan Bilzerian to be a professional poker player. Although exact figures are not clear, he has been a part of the poker high roller scene and has made money in poker.
However, he is definitely not one of the best poker players, or close to the ability of many poker professionals who dedicate their lives solely to poker. In contrast, Bilzerian is more of a businessman, with many different entrepreneurial ventures in different industries currently occupying a lot of his time.