The protesters in the article seem to conflate one kind of construction with the other: "The protesters say the city should house the neighborhood’s homeless people before it approves another big residential development in downtown Los Angeles."
Market-rate development is a process that can continue to take place while the city grapples with housing the homeless. They don't interfere with one another, since the market-rate construction is private enterprise.
The protesters, further, are falling victim to the same fallacy discussed in the original posted article here: "They also argued that hundreds of new market rate apartments will drive the neighborhood’s rents beyond the means of residents living “precariously” in nearby converted flophouses, hotels, tents and buildings."
The basics of trickle-down housing dynamics work strictly against the rising rents scenario being true. The pressure goes strictly the other way for the existing units in the neighborhood, which have new competition at the top end.
Here is the first news story I found on Google about the subject.
http://www.latimes.com/local/lanow/la-me-ln-skid-row-tower-2...