Plumbing venting into apartment
That bit of plumbing where the pipe does a U shape before going down, that is called a trap.  

Every drain has one.  Think about what happens when water goes down that drain regularly. The water can't all get over the hump, so it stays down in the U-shaped area.  This has the effect of plugging the pipe.  The whole point is to stop sewer gases escaping.  

Now, think about what happens when water doesn't go down that drain regularly.   That "plug" of water dries up.  Voila, the pipe is now wide-open and stink ensues.  

The cure is to pour water down that drain.

The water will be trapped in the U-part, and provide the sewer gas plug as intended. 

As you can imagine, it only takes months for that water to dry out, so it has to be done again from time to time. And it will happen to any drain or sink that is disused.  So you should be prepared to do it as often as needed. 

Or you can properly cap the line with actual pipe fittings that clamp or screw in, readily available at the hardware store. 

Whose responsiblity is it?  Let's see.  That fixture appears to be intended for a washing machine, so it is a "feature" not a "defect". Even if it was a defect, do you really want the landlord coming into your home every 3 months to dump water down each trap?  I would argue the traps should be maintained by the tenant.