I am trying to program a TFT LCD Display with an ITEK ILI9163C Driver attached. Is this the correct software to program this controller?
The Key MDK-ARM tools can be used to program devices that has a supported ARM core. It will then be up to _you_ if you will manage to make the ARM core perform the actions needed to handle different hardware interfacing internally/externally to the core.
If you have pen and paper, that isn't enough to answer if you will be able to produce an opera or a New York Times best seller.
Note that you made your post specifying "Toolset None". If you have a Z80 processor, you need tools suited for a Z80 processor. But the Keil ARM tools doesn't support Z80 processors. If you instead use a 8051-compatible device, you need tools that supports 8051-compatible chips. But the Keil ARM tools doesn't support 8015-based chips. If you instead have an ARM processor, you need tools that supports that. In that case, the Keil MDK-ARM might be a good choice. Just that you still have never mentioned what processor you have - Keil MDK-ARM is not a good choice for a 64-bit quad-core ARM chip. And you don't want to port the Linux kernel when it is so much easier to use gcc with such a processor.
If you specified "Toolset None", because you wondered specifically about the editor in "Keil ARM uVision", then the editor can be used with a huge number of different processors, if you just use it together with a compiler tool chain suitable for your processor.
So in the end: It isn't the Keil tools that seems to be the weak link here, which means we can't answer your question based on the information you have posted.
The processor is: STM32F103RET6 ARM 32 bit Cortex-M3