Since Warlords of Draenor, there have been multiple Hearthstone reference added to the game:
- You can buy items related to Hearthstone from a NPC named Benjamin Brode in your Garrison. He is named after and is a tribute to Ben Brode, the Hearthstone Senior Game Designer. You can buy from him:
- A Winning Hand (Use: Show everyone that you just won a game of Hearthstone! (2 Min Cooldown))
- The Hearthstone Board (Use: Throw down a Hearthstone board, letting everyone know you're ready to play! (3 Min Cooldown))
- There's a rare Garrison mission called Hearthstone Tournament available for your subjects which will reward you of:
- Autographed Hearthstone Card ((Use: Turn the card over to see what you got! (10 Sec Cooldown)) "Signed by Trump and Reckful. Not too shabby.")
- Hearthstone Strategy Guide (Use: Teaches a follower the Hearthstone Pro trait. "Transforms an ordinary follower into a tactical genius.")
- The related trait Hearthstone Pro which can only be learned with the above book and gives additional XP to your subject during the missions.
Thus, we could safely conclude that Blizzard is kind of trying to add Hearthstone to the lore of their Word of Warcraft game by implying that Hearthstone games are played mainly in Orgrimmar, Stormwind, Stranglethorn and Pandaria (out of the four boardgames currently availables).
But those are still easter eggs at their current states, as we've never actually seen NPC playing Hearthstone in the game. It seems a bit weird that the common NPC would be playing as Jaina against Thrall, using demonic and draconic entities. (But Blizzard's NPCs are always a bit off so it's a possibility nonetheless.)
It's more of an opinion-based at the moment but I'd say it would be accurate to add this in a Role Play lore or assume people are playing Hearthstone in Stormwind's inns, thanks to the easter eggs added by Blizzard.
Thanks to Michael Hampton for pointing that out: there's a game actually being played between Merra Finklestorm and Waina Steelpaw in front of the Shrine of the Seven Star (and probably at the Horde counterpart too). We can't talk to them but they sometimes let out things like "I need to rebuild my deck". There's probably other players in other cities too.
And as many have said, it's not stricly speaking "a game within a game" which could be played through World of Warcraft, but it is nonetheless a game that does take place within the World of Warcraft universe (which was the original question the OP asked for).