Similar batteries are in the motorcycle market right now. I am running a LiPFeO (usually goes by the name of "Lithium Iron") in a motorcycle right now. It is a drop in replacement and works on a standard 12V system. From reading the website they are doing there best to hide what technology they are using. So I can only guess based on all the research I did in the past.
Compromises? Yes! It has exceptional cranking capacity but reserve capacity is horrid. So long as the starter starts the engine, you are doing great. But they go dead fast if you put a sustained load on them. Listen to a radio with the engine off, winching a dead engine truck, not a good plan.
Cold weather. Things get interesting. The internal resistance goes up as the temp goes down. They are not good cold batteries. The motorcycle trick is to turn the key on and run the headlight for a minute or two. This loads the battery, the internal resistance warms the battery up and the bike will now start. But if you go straight to the starter button, they are known for a slow crank in the cold.
Do not run them flat, the cells will not recover. While not good for lead acid, you lose some capacity running them dead it will pretty much totally kill a Lithium Iron.
As for that button for an emergency start. Looks to be an internal disconnect override.
Does the battery work? Listen to that diesel start at the end of the show. That wasn't exactly a great sound as the engine started to crank. Sounds like it is lacking a bit of cold cranking capacity.
Would I run one? well I am on the motorcycle. But the battery in that is optional, it will start and run without one. In a race car to save weight, sure I would run one. Something with a winch? No. A daily driver? Probably not. Would I use this company? No. They are hiding there battery technology to make it non-comparable to other batteries on the market. There are batteries on the market with a track record. For the Bike I have a Shorai.
The battery is different. You have to be aware of that and learn to live within the limits of the new technology. Didn't say bad, just different. We are well versed in what lead acid does and have adapted to its abilities. Lithium Iron just has different properties.