The games have attracted criticism from Democrats.
Matt Lesser, a Connecticut state senator, said: “Heating oil is near an all-time high but, hey, you can play border tsar Tom Homan in a video game.”
Jessica González, a Texas Democratic state representative, wrote: “Trump’s White House literally built video games on a government website before doing anything to solve America’s affordability crisis.”
Adriana Jasso, programme co-ordinator for a border volunteer group, said the arcade-style games showed a fundamental “lack of seriousness” by the White House.
Ms Jasso said: “The cruelty, the extremity of the administration … is no longer surprising. This presents the issue as if it were a game, when in fact it is not.”
The White House said in a statement: “This administration is laser-focused on ways to innovate and tell the story of the president’s many accomplishments in a way that resonates with every American.
“This is an effort to further contrast between a culture of fun and winning and the dark socialist vision Democrats have for America.”
The Telegraph has approached Sega for comment.
