The manga has the drawing of the Rasengan on one of the colors yellow, and the games says it is blue. I think it's yellow because I believe the manga is canon. What is the actual canon color of the Rasengan?
Strictly speaking, the canonical color of the Rasengan should be yellow, because Naruto's chakra is yellow in the manga. (Chapter 91)
The anime changed the chakra color to blue for some reason, probably because they felt blue looked better in the animation. Games are often made to resemble the anime, not the manga, so that could be the reason they picked blue.
The yellow image in the anime that you mention is an inconsistency. They may have used the color from the manga for that image because it wasn't important for the plot.
The rasengan is blue because pure chakra appears blue to the human eye. Despite naruto's nine tail chakra being orange he does not utilize this chakra when using the jutsu hence the rasengan takes the form of a blue rotating orb.
However it has taken multiple colors before in the anime and manga and this is because of what chakra is used to create the jutsu.