The generated content is the data that will be sent to the TV for processing.
You don't appear to have considered the most basic requirements.
You send composite video or HDMI signals to a TV. That has to be done continuously at a fixed rate.
For a basic analog system such as old-style video games with composite or component video out, to run as just 640x480 pixels graphics and 25/30 frames per second, you need to move around 13 million pixels data per second, with anything from one to three bytes per pixel if you want colour.
A 640x480 display needs 307,200 pixels.
At just one bit per pixel (monochrome, no grey scale) you can just do in in some very! fast MCUs, using almost 40K Bytes RAM.
If you want colour packed in to 8 bits, that jumps to 307 KBytes; for 24 bit colour, multiply by three, so roughly a megabyte.
For any HDMI video out you need dedicated HDMI capable hardware.
The ATMega has only 2K ram and an 8 bit CPU with not a fraction of the speed required.
This design is outputting a character-only display using a single IC MCU - the most minimal design I've ever seen; it uses a 32 bit CPU capable of running at 50MHz has 32K RAM built in, costing under 10-
It uses the serial hardware to output a one-bit video stream.
ps. I never suggested using a Raspberry Pi board - I said use the CPU.
Even the one used in the Pi Nano can be set up to produce a basic analog colour video signal - at 82 pence or roughly $1 each..
Order today, ships today. SC0914(13) – ARM® Cortex®-M0+ series Microcontroller IC 32-Bit Dual-Core 133MHz External Program Memory 56-QFN (7x7) from Raspberry Pi. Pricing and Availability on millions of electronic components from Digi-Key Electronics.
Info on using that:
The more powerful Pi CPUs with full GPU included as used on the more powerful Pi's are more expensive, but vastly more powerful and can produce HDMI video.
And note that old consoles like the Famicom / NES & early home computers with graphics, that had 8 bit CPUs, always had a dedicated video IC, often custom designed, to output video.
Ones with anything above ASCII graphics used hardware sprite generators that allowed tiny bitmaps to be positioned at any start pixel, without needing massive RAM to do it; they did not have true any-pixel-any-colour capability, as that needs more RAM than was practical back then.