What are the thermonuclear bombs for? It looks like they think they mean to induce heating with the bombs, but that would be a miniscule amount of energy compared to the total energy budget of the planet.
Mars's atmosphere is already mostly carbon dioxide. Somehow adding more will cause the upper layers to be ripped off by the solar wind. That mechanism is why Mars's atmosphere is so thin already.
Methane is lighter molecule than carbon dioxide. It is a better greenhouse gas, because it's molecule has more degrees of freedom, but it will zoom to the top of the atmosphere, get ionized, then blasted off into space.
Let's pretend that the planet is warmer, so we can keep talking about the video...
Water ice melts... Sure... Because we created that heat pulse. The water becomes vapor, and starts getting stripped out of the upper atmophere, just like it does on Venus.
Bombarding the surface with comets, sure, they have a lot of water. Asteroids? Some have water, some don't. I might be splitting hairs here, but there isn't a lot of reason to go after asteroids unless you want the metals. If you just want water, stick to comets. You can find them in helpful orbits already. Also keep in mind you will loose material back into space because the force of the collisions are strong enough to produce ejecta traveling at escape velocity.
I like GMOs just fine, but turning carbon dioxide into oxygen is what all plants do. Why modify them? To include a buzzword?
What is the job of the GMO microbes?
3D printers to make the house. Sure. That sounds good. Did anyone do a trade study vs. other construction techniques?
And finally we most some humans on to a planet whose atmosphere is being ripped off at an alarming rate. Maybe we'll get a good couple hundred years out of this... Except, there is no appreciable magnetic field, so all those crazy charged particles that make auroras on Earth, will instead come slamming down on the residents' DNA.
I wouldn't do this.

The Martian atmosphere has mass of about 2.5x10**16kg and a loss rate, from Mars Maven observations of about 0.1kg/s. Loss estimates of the relatively non volatile element, Argon, indicate a 65% loss over time. But clearly, Mars once had a much higher surface pressure, higher surface temperatures, and large bodies of liquid water on the surface, especially in the northern hemisphere. Past loss rates were likely much higher from a more active sun. In either event, you would have to account for a loss rate of about 3m kg/yr. ???

Where does the CO2 come from?
From where or how to transport the sizable about of methane required?
How do you redirect comets to hit Mars?
How do you prevent solar flares from stripping the atmosphere since Mars has no magnetic shielding?

Good idea nuke it until it glows so it will never be habitable.
Anyway water isn't a problem since 1/3 of the surface is covered in ice sheets up to m thick, see [science.sciencemag.org].

A beter option is to seed with constructors to build domes and mine material. The constructors would build others. James Hogan wrote a novel along this line called Code of the Life Maker.

The intial constructors will need supply of things from Earth, mostly integrated chips, cpus and asics.. most raw materials should be mars-sourced.

One very interesting science project would be a radio interferometer linked to earth. (Although L3, 4, and 5 would be better but more to service...) this observatory could image every stellar object in the Milky Way and it's satelite galaxy.

I love Hashem's videos! The idea of terraforming Mars is fascinating. I wonder if I'll live long enough to see it happen.