This is not a trivial task and there is not a single chip solution available.
Things you need to consider...
What is the compressed video format coming from the Ethernet?
What protocol is the video being streamed/sent in?
Is the video streaming or file based (real time/non-real time)?
What is the compressed video resolution?
Do you need to scale different resolutions to NTSC/PAL resolutions?
Do you need to support frame rate conversion?
Do you need to support a single format or multiple formats?
Do you need security?
Do you need encryption/decryption?
Do you need audio?
What audio formats?
Do you need to support compressed audio (AC3, DTS etc...)?
Once the processor receives the compressed video it will need to decode the compressed video/audio then potentially scale the video ready to be sent out through a NTSC/PAL video encoder and audio DAC.
One potential processor is the DM355. Other devices in this family can support higher resolutions than NTSC both in compressed video decode performance and display hardware resolutions.
Processors in the DM385/DM816x/DM814x families can support multiple streams at full 1080p60 on multiple displays.
BR,
Steve