The short answer is yes  poker still falls under the category of gambling, despite its status as a game of skill. Consider the Merriam-Webster Dictionary definition of gambling: Gambling  the practice or activity of betting; the practice of risking money or other stakes in a game or bet.
Poker has a gambling element to it, which leads some players to question if poker is just down to luck. Although there is a serious amount of luck involved in poker, the fact the same big names regularly win in cash games and tournaments shows that there is skill involved.