A couple of things on this interesting development.
The article states: "Providence paid $150 million for a 25 percent stake in 2012. Six teams have joined MLS since then, diluting Providence’s original share." I think that means two things. First, the new teams get a stake in SUM in exchange for their franchise fee, which diluted Providence. Second, Providence probably got a portion of each franchise fee in exchange for that dilution - and this contributed to the return they made on that $150 million.
It's really tough to figure out what stake Providence had in the end - and therefore the value of the entity for a couple of reasons. For one thing, we don't know how much each additional team diluted Providence. More importantly, we don't know whether ownership is limited to MLS and Providence or whether others share ownership. While the article states that Providence is the only "outside" owner, remember that SUM controls marketing for other entities as well, U.S. Soccer in particular. It is possible that they hold some ownership.
Finally, it's worth highlighting this line from the article: "the league [MLS], which is eager to capitalize on the growing interest in U.S. soccer around the world." If that's an accurate representation of MLS's motivation, it means this isn't just to capture additional expansion fees and domestic rights. It is because they think they can make good money selling MLS overseas in coming years. This makes sense. I am not sure when foreign rights come up for renegotiation, but the domestic rights are locked in for a while. Overseas, we do know the league's reputation is growing, and the fact that it is playing now - when other leagues are off - has to make it very appealing to broadcasters.