Streetcars traveled down Grand Avenue to Navy Pier. The C&NW line to Navy Pier ran alongside the north end of the North Pier Terminal buildings in the background on Illinois Street. The track in the foreground with the boxcars shown in the view that was just posted for this topic looks like a spur. That would be my guess as well, that the spur is for construction materials. Looks also like the areas on both sides of LSD were leveled.
Here's a view showing the line to Navy Pier when it was still in place but out of service alongside the North Pier Terminal building.
http://www.chicagoswitching.com/chicago/former-cnw-up/navy-pier-line/Navy-Pier/Interesting in this view to see that the builders of Lake Shore Drive had to chop off part of the North Pier Terminal building to create access.