TWR-VF65GS10, how to programm?
I can't speak for the STM32F7xx or Sitara, but you do not need to use embedded Linux for a VF65 Vybrid board.
I've been working with a Vybrid based device for about 3 years and I was responsible for porting the existing firmware from a Kinetis K70 to the Vybrid.
The TWR demo board you're looking at has the dual core Vybrid with both A5 and M4 cores in the chip, and it's not clear from your question if you're intending to use one or both of them.
In our application I ignored the M4 because in our production device we would be manufacturing with the A5- only version of the chip.
Our firmware uses a very lightweight OS (CTL from Rowley Crossworks) and we've written all of our own low-level driver code, and although an OS of any sort is not required I think it would be difficult to take advantage of a chip like the Vybrid without one.
The biggest learning curve for me when transitioning from a smaller micro to the Vybrid was the fact that it has no on-board Flash memory, so all of your code lives in external Flash (ours has external QuadSPI, but there are many different options).
We also have 256MB of external DDR SDRAM and at power up all of the code is copied over from the QuadSPI flash to the external RAM and executed from there (we're using most of the internal SRAM for a framebuffer for our display).
If you're already familiar with something like FreeRTOS and the HAL libraries you shouldn't have too much trouble implementing them on a Vybrid.