John Wick in this article says: “roleplaying game: a game in which the players are rewarded for making choices that are consistent with the character’s motivations or further the plot of the story.”
So, what is the reward?
'roleplaying game' is defined differently by various groups of people in different times. Distinctions between roleplaying games, as defined by these people, and other games (e.g. card games) these people might or might not play, may change.
Just because Gary Gygax said something about Dungeons&Dragons doesn't mean anything to a German gamer playing Das Schwarze Auge.
If you're serious about defining roleplaying game, then find out who used the term in which context, and when, and where. Do research.
So, we know now what John Wick, the RPGPundit, and others
Does any of this matter to my game?
Does my opinion matter to yours?
In order to play the role of a character, the player must have the opportunity to make meaningful choices within the game. Quite a few game situations present the character with a double-bind: fight1, or fight2. It doesn't matter whether they fight with fists, thumbs, tea cups, or lightsabers. They need different options. The players then will get rewarded by enjoying their decisions, and the consequences of their characters' actions.
So, to make the game more roleplaying-ish create situations where all the characters (monsters, too) act not according to the standard protocol: fight1, or fight2.
Roleplaying games are like thought experiments: What would happen, if ...? How could a character act, if ...? How likely is the character to act one way, or another?
Find plausible solutions for a given situation within the limits of the character's role, and means.
And yes, you can turn chess into a roleplaying game. Because, just as with D&D, who cares who designed it for what! It's my game, when I play it.