Why is Unix still used if Linux is based off of it, and Linux is free?
Both questions are misguided, for different reasons.
People still use Unices because they tend to have large, "well-established" companies behind them that they can turn to in a pinch (yes, I realize that this is mostly a fallacy at this point, but I'm not the one you need to convince).
Unices have no need to "keep up", since GNOME, KDE, etc. are for the most part built against POSIX rather than Linux. You could potentially build and run them natively on AIX if you really wanted to.
Let me throw in some more arguments why the transition is rather slow (but there is definitely one):
First of all it is sometimes very difficult for Customers to switch from one UNIX vendor to another. Even if you jump from, let's say, SuSE to RedHat, there are plenty of things that differ from an administrator's point of view. When going from an AIX (or HP/UX or Solaris ...) to any Linux, things differ even more. As a customer you have to check whether it pays off to migrate your environment.
Normally there's a whole bunch of 3rd party software involved and it's not a trivial task to verify if everything is available for the target environment. If software has to be replaced due to the OS migration it has to be checked whether it is compatible with the existing company framework.
If self-developed software is involved, the SW has to be ported. Often this fails immediately at step #1: The target OS has not all the needed libraries or the used development framework.
Also it's not very cheap to train the SysOp and SysEng teams to a new platform. Years of experience may be rendered worthless (depending on the depth of experience), new best practices have to be (re-)evaluated and some SysEngs may even leave the company because they want to go on with their *NIX derivate instead of switching.
The total cost of a migration is immense in large environments. You may easily calculate 1-2 years of planning, doing, UAT test, stability tests, disaster tests - all involving a lot of people (all of who want to be paid) which are drawn away from their daily tasks.
Considering all this, one may understand why companies stay with their current vendor and prefer just to upgrade existing environments. From what I've experienced, new systems get their chance when it comes to building up new environments.
But after all: there aren't many ClosedSource-Unices left out there. AIX, HP/UX and Solaris are the big vendors left (OS/X if you count Desktop systems in). As I think of it, I even don't know if IRIS is still alive...
I've removed already written sentences about that user-interface saying before hitting the post-button as this would end up in a flame war :-)
I think you have the misconception that 'UNIX' is a specific product that you can go out and buy. Today, UNIX refers to several families of operating systems.