I just finished working with a company that has had several very successful Kickstarters.
IMHO, lighting and audio are more important than camera type for this type of video, as long as you have a pro-sumer camera that shoots decent 1080p HD. Many successful campaigns have been shot on a DSLR with a stock lens. If you want to buy an additional lens then your first lens should be a "nifty-fifty".
An external microphone is way more important than camera.
Here is the one piece of advice that was given to me by someone that has run mutltiple multi-million dollar Kickstarters. Don't let someone that is dry and boring be the spokesperson for the video.
Of course the owner/CEO of the video wants to be in the video, but that's not always the best choice to be the talking head. Instead use them in action scenes, Like at a workbench or a design table.
I re-read your post. I assumed it came with a kit lens and you were wanting to know if you should upgrade the lens. The poster above is correct, you have to have a lens. But what I don't understand is why are you going with such a high-end DSLR?
The camera you are looking at, the Nikon D7200D, is a great camera. But it's also an overkill for what you need. It's a 24MP camera that can shoot video at 60FPS. HD video is only 1.8 MegaPixels and you only need 30FPS. For almost the same price as the rental of the body and lens you could buy an older model (refurbished or used) DSLR with a 50mm lens and own it. This would give you time to learn how the lens AND the camera work since they are two different beasts.
Also because a DSLR is not primarily a video camera, it's actually a little bit more complex to setup for video. Not ideal for a beginner. A Pro-sumer HD video camera would be a better choice but it costs more.
So I would actually recommended, for a beginner, a camera with a built in lens. Something like a Nikon Coolpix that shoots full 1080p. You can definitely get one of those (factory refurbished) for less than what you would pay to rent the Nikon D7200D with a lens.
I know I'll probably get criticized for that recommendation. But if you don't know how to use the D7200D, then you probably won't shoot anything better than would with a Coolpix.
Now all you need to do is learn 3 point lighting. If you put a key-light on the back of your subjects head, then you will shoot something better than most other kickstarters.