At the time, the story was Trump's fallacious claims that there was widespread voting fraud and tampering with voting machines. The implication was that there were millions of illegitimate votes for his opponent. There was no justification for his view that it was possible, or even if it was, that all fraud would favor the Dems.
The context of this hacking is mostly of voter databases. This information can be used for propaganda campaigns, and other kinds of targeted attacks that suppress voter turnout, intimidate, and sew distrust in the system.
> In Illinois, investigators found evidence that cyber intruders tried to delete or alter voter data
Which implies that voter registration lists may have been affected.
During the primary elections, there were reports in certain states of people who found their names missing from the voter lists and had to cast provisional ballots. (Anecdotally, I know at least one person who votes regularly and found their name missing, despite not having moved or changed their registration information since the previous election, only a few months before).
From the article, we can't say if those are related, but it's clear tampering with voter registration information was the intention, whether or not they actually succeeded:
> In fact, the Obama administration believed that the Russians were possibly preparing to delete voter registration information or slow vote tallying in order to undermine confidence in the election. That effort went far beyond the carefully timed release of private communications by individuals and parties
Well he wasn't completely wrong there:
Then Trump won the election, and Russia's meddling (and I'm certainly not saying that they weren't) became the go-to excuse instead of addressing the various 800-pound gorillas in the DNC room.
This is merely a continuation upon that theme: that if it weren't for a third party's involvement, Hillary Clinton would be the 45th President of the United States, therefore the current Chief Executive is less-than-legitimate.
This is all about political posturing; in four years, the voting process will be no more secure than it is today.