I don't think they would work on Mars. First the timescale is hugely sped up. Mars society estimates a thousand years to get to a point where the air is thick enough for trees to grow and humans to be able to survive without pressure suits with an aqualung type closed system breathing apparatus. And it could be thousands, even hundred thousands of years, to get to an oxygen rich atmosphere.
Carbon dioxide is poisonous to humans above 1% concentration in the atmosphere, even with plenty of oxygen. And it depends on there being enough CO2 for the atmosphere to go into a runaway greenhouse effect.
It's not at all clear if there is enough. For a runaway effect you need 10% of Earth's atmospheric pressure. There is enough known for 2% of Earth's atmospheric pressure.
The amount of energy needed to liberate dry ice is huge. About a billion megatons of energy to double the atmospheric pressure or about nine billion to get to the 10% concentration where a runaway greenhouse could start up.
If you deliver that much energy to Mars, that's a rate of several megatons of energy you need to supply every second, all just going into making the dry ice sublimate - never mind warming it up, or the ice, or the regolith and ignoring all losses into space.
His techniques would generate several orders of magnitude too little energy to do much to the climate of Mars.
Which is no surprise. Look at Earth. It takes billions of people driving cars and burning coal for decades, to make a difference to the temperature of the Earth of one degree. And indeed the "easiest" way to warm up Mars is probably to create artificial greenhouse gases using fluorite ore. But that is still a mega project. It's eleven cubic kilometers of fluorite ore you need to mine, and it requires the output of 200 nuclear power stations running for a century, just making greenhouse gases as the only thing they do with all that power. And it only works if Mars has enough CO2. And there's lots to go wrong along the way.
Earth's atmosphere is not nearly warm enough for Mars even if you could duplicate it magically on Mars. If you manage to get rid of all the CO2 and replace by nitrogen and oxygen, take the carbon out of the atmosphere so it is breathable - then you are committed to stepped up levels of greenhouse gases for all the future to stop it from getting as cold as Antarctica.
For the energy requirements see my article: Why Nukes Can't Terraform Mars - Pack Less Punch Than A Comet Collision
For other issues see my article: Trouble With Terraforming Mars