Halo 3: OSDT
Halo: CE Anniversary
Halo Wars, Halo 2 (PC), Spartan Assault, is not a real Halo or Achievements Game because first of all Halo Wars is not a FPS Halo game also Bungie never made the game look on the back of the game box, Halo 2 was a xbox game ported to (pc) xbox game don't have achievement back in day, And Spartan Assault is really a Window 8 game ported to xbox 360/xbox one/Window Phone.
I would first like to say congrats on the gamerscore you have acquired throughout your Halo career!
I unfortunately have to disagree with what you said about several games not being a real Halo game. Halo does not have to be limited to a FPS. I agree that the FPS Halo games, especially the Master Chief games, are the core Halo games. This does not mean that Halo is limited to just this.
Just because Halo Wars is not a FPS does not mean it is not a true Halo game. It provided a great story that is up to par with most of the other Halo games and was an enjoyable game to play. Also, just because Bungie didn't create the game does not mean it isn't a Halo game. Halo 4 was developed by 343 Industries and not Bungie and Halo 4 is definitely a Halo game.
Halo 2 (PC) is a tricky one. It is definitely a Halo game and it has achievements. It didn't have achievements when it was initially released but that doesn't mean it can't now. GTA: San Andreas was just released on Xbox 360 with achievements. However, 343 decided not to include Halo 2 (PC) achievements in their total Halo gamerscore counter so I respect their decision about this and do not include my Halo 2 (PC) achievements in my total Halo gamerscore. If I did, I would be sitting at 11300 Halo gamerscore.
Finally, Halo: Spartan Assault is a Halo game as well. Just because it was originally a Windows 8/Windows 8 Phone game that was later ported to Xbox 360/Xbox One does not mean this isn't a Halo game. A spiritual successor, Halo: Spartan Strike, is being released this December. If 343 didn't consider Spartan Assault to be a Halo game, why develop another game like it? Also, Halo: The Master Chief Collection are all Halo games being ported to the Xbox One and they are getting achievements as well.
Overall, all these games are considered Halo games. It is great to see that you enjoy to play Halo by looking at your gamerscore but it saddens me to see that you don't think some games can be Halo games either.