this is more, "transmitting SDI signals from a GS2962 driven by an FPGA with some high-level control by an Arduino". An AVR chip isn't going to blast out 1080p30 out of its GPIOs any time soon.
The notion that an Arduino has to be (just) an AVR chip is wrong though. The board in question here is an Arduino MKR Vidor 4000 (which doesn't even contain an AVR chip, the SAMD21 is a 32bit ARM Cortex M0) and you also have the Arduino 101 which has a x86 Intel Quark microcontroller. Most of the new Arduino products are using 32 bit ARM processors now.
But Arduino (the company) is _most_ famous for their use of the atmega-based products, and "Arduino" (the word) is often used synonymously with those specific products (and often specifically meaning the Arduino Uno). Their non-atmega products are a newer and less popular development. I'm sure that over time "Arduino" (the word) will be used less and less to mean one of their atmega products, but for a lot of people, "Arduino" still means "board with an atmega328p".
I would personally hazard the guess that for a significant portion of the people who use Arduino, it just means any board that is programmed in the Arduino framework. They have no real idea about or connection to the hardware that is running their code.