carbonated water is good for you in that it's water, and the first minute of that video is chemically accurate information, but after that it's all theories that are very similar to the recent alkalinity craze, attributing most of the things he's talking about to an alkaline pH level instead of an acidic pH level in your blood.
blood pH level resets extremely quickly, often within minutes, so a lot of the benefits he's talking about wouldn't be gotten by drinking carbonated water unless you were drinking vast quantities all day(probably enough to be disruptive) considering the relative amount of liquid in your body and the rapidity with which your body balances internal pH level (it has to rapidly return to homeostasis or every time you ate something. your pH level would be thrown off and your organs would be chemically burned).
as far as the co2 baths themselves, your skin is an impermeable membrane, so you aren't getting CO2 benefits in your organs like he's talking about, except maybe as a second hand effect from the CO2 being released into the air from those baths, but again, that would be extremely minor and your body would stabilize that acidity within minutes.
All of that said, I like sparkling water and drink it because I feel like I'm having a treat but there's no sugar or anything else so I think they're good drinks in any case, but there is no data saying that drinking carbonated water is a good thing outside of being water, as this guy casually admits before theorizing and implying conclusions about the virtues of drinking carbonated water, leading to having more acidic blood. that's whackadoo.