I rent my apt as well and you can make an NIC cage without having power tools and such. It usually requires zip ties, NIC shelving cubes, toenail clippers or scissors to trim the zip ties, a file to file off sharp edges (I use the one on the nail file), and somewhat of an idea what you're building.
You could even use a fold-up exercise pen made for dogs that would be adjustable to fit the room (circular, square, rectangle, etc) without costing as much as a tiny store bought cage. If you have wood floors or laminate you can put down towels or something to protect the floors. I have carpet so I bought discounted pop-together laminate and put that over my carpet, then put an exercise pen on top of it for my two rabbits. It's easy to clean and gives enough space when I can't let them out all day.
I'd say that cage is too tall without having enough width/depth for a rabbit. It looks more like a good two-three rat cage since they are much better climbers.