If Shkreli wasn't in prison, then he would be a normal "activist investor" who has the ownership (power) to dictate corporate strategy at the highest levels. Whether he's the chief executive or not is kind of a moot point—that's just a title.
If I recall correctly, a securities-related conviction would prevent him from being a director of a publicly-traded company. But Phoenixus AG (née Turing) isn't public, so I don't think there's SEC limitations here.
That other shareholders want him removed from power is a preference and disagreement, nothing more.
Was there anything else in his sentencing that would preclude him from these kinds of activities? Or is this more a, huh, that's interesting message?
Reading the article, it seems like the rules he's breaking are:
1. Having a cell phone in prison.
2. "Running a business", in potential violation of the prison inmate handbook. I'm unclear if there are any legal teeth behind said handbook, or what.
The article also says that the FBI "has interviewed associates about his role" at Phoenixus, but not why they're doing that.