No, it's not legit (in the sense you used the word). Perhaps the file won't appear inside their application, but doesn't mean that nobody else will be able to open it again.
- “Favorite” files so you can access them offline
Ok. You install their program in some computer, mark the file as favorite, and it's downloaded to that program. Then you disconnect from internet, and you can still access the file.
- UNshare™ gives you the power to instantly revoke access to files you've already shared, even after they’ve been downloaded
In the offline? If the computer is never again connected to the internet, this access will never be revoked (since there's no way to know/download that revocation). If it's based on time, simple enough, adjust the computer date/time to the same date/time  . It's based on number of accesses? Create a virtual machine (VM), install/download inside that VM, create a snapshot of it, and rollback to the same snapshot when you need it again .
In the online mode? After I download the file inside the program, to be useful somehow, I need to execute it or open it with other program (think of some image). After I open it with some other program, just click in the "save as..." and, voilà, I have a copy that cannot be "unshared" . Or create the VM and take a snapshot when the file is opened inside some program, or executed . Or install some program that will capture the stream of bytes right after it leaves the "unShare program" .
- Set permission levels and prevent printing, forwarding, and screen-grabs
While inside their program, perhaps you can prevent printing and forwarding. After it leaves their program, it's up to the program using the file (like PDF reader) that will prevent such thing.
Screen-grab: take your camera and take a picture of the screen. Done. Install some program that will work with the video driver, and that will take screenshots every x seconds. Done.  
- Delete synced data on devices that you no longer control
Yep, if the device is online, send some command to their program that will erase the data. Turn the internet access, and this functionality is gone.
Edit after answer accepted:
Even easier to answer: the company says in their EULA:
When an End User accesses data on the Service (e.g., a publication, comment, or attachments to a publication or comment), a copy of that data is copied to that user's local computer (this is called "caching" and is part of how web browsers work). Caching is used to improve the speed of the Service when you repeatedly access graphics or data during a session. Once pages and/or data have been cached on your local computer that data is beyond the control of Intralinks, and may be accessible to anyone with access to your computer. Each End User assumes all risk and liability associated with any data cached to that End User's local computer.
(I added the bold emphasis to parts of it).
So, they say that the data can be leaked by browser cache. Even easier to circumvent their protection.