In general, the Injustice comics are considered canon to the game. They often provide additional background and depth to the game's universe, filling in plot holes and enriching the characters' arcs.
The Injustice game has a resemblance to the comics. It features familiar characters and plot points, but also adds some unique elements and gameplay mechanics to stand out.
The Injustice Game Story is centered around a twisted version of the DC universe. Superman, after the death of Lois Lane, becomes a dictator - like figure. He starts to enforce his own version of justice which many heroes find unacceptable. Batman, being the strategist he is, tries to assemble a team to oppose Superman. The story shows how far a hero can fall and how others will rise to stop them when their actions cross the line.
In most cases, the Injustice comic is placed in a timeline that follows the game. It adds depth and further developments to the characters and their situations.
Sure, the Injustice comic takes place after the game. It builds upon the established setting and characters, introducing fresh challenges and story elements that continue the overall narrative.