It seems a really obscure 1987 case for a presidential pardon:
Two years of probation and fined $250 Working at an illegal gambling parlor
Is there a political angle to this pardon?
Politics Stack Exchange is a question and answer site for people interested in governments, policies, and political processes. It only takes a minute to sign up.Sign up to join this community
In the USA, a conviction is likely to affect your rights for the rest of your life. This is unlike other countries in which you retain or regain rights after a set period of time.
So, Mr Takumi may have lost the right to vote, own a gun, act as an attorney or a financial advisor. For Takumi, who now works as a tax advisor within the Navajo Nation, this last could be a significant restriction. The only way for him to regain his rights is through a presidential pardon.
The purpose of the pardon was indicated by a White house source:
"Through these full and unconditional pardons, the Federal rights of [Takumi and others], including the right to vote and the right to bear arms, have been fully restored, Today, they are once again full and equal citizens under the law."
It is precisely because this was an obscure and ancient case that was having a disproportionate affect on an individual that the President granted a pardon. There does not appear to be a political angle.
Well, it's not incredibly clear what may have been the main reason(s) in this case, but I disagree there's no political angle whatsoever, as asserted in the other answer.
Trump has already established a pattern of pardoning minority members apparently as a way to ingratiate himself politically with minorities, e.g.
On Wednesday, June 7, President Donald Trump commuted the life sentence of Alice Johnson, 63, who was convicted for a first-time, nonviolent drug offense. [...]
Trump already posthumously pardoned the black boxer Jack Johnson, convicted for driving a white woman companion across state lines [...]
Trump even told reporters today that he’s considering pardoning Muhammad Ali, a prospective offer met by the Ali family’s lawyer with an enlightened response that there is no pardon to give. While Ali was convicted in 1967 of draft dodging after refusing to report to fight in the Vietnam War, the Supreme Court unanimously overturned that conviction in 1971, making Trump’s offer moot.
Presidents have always used pardons as political favors. But Trump’s pardons of both Johnsons (and his offhand pardon offer for Ali) are clearly aimed at gaining approval among black voters. Trump tweeted a picture of himself and Kardashian West, who has a massive black following, after their meeting regarding Alice Johnson. Trump could not be more explicit that his relationship with Kim’s husband Kanye bolsters his credibility among black voters.
It's less clear to me how important politically the Navajo Nation is to Trump (compared to African Americans), but interestingly his administration has been in a couple of disputes with the Navajo Nation, one involving the Bears Ears monument, regarding which according to LA Times
Trump opted to shrink the monument to about 200,000 acres, potentially opening hundreds of thousands of acres to mining operations
and another on the planned closure of an agency (still) dealing with a 1974 relocation of Navajo families.
The fact that Trump pardoned a member of the Navajo Nation in this larger context may be entirely coincidental... or not. Unlike in the Johnson (or other African American) case(s), Trump hasn't tried to overtly exploit politically his pardon of Takumi, as far I can tell.