I haven't used one but am fairly familiar with the tech. They use a boost SMPS to put the voltage up around 14V to charge the caps then switch the circuit to discharge the caps.
It can work fine, if you buy a unit with enough capacitance for your engine size and "IF" the battery has a little charge left in it, but if the primary problem is the battery is shot rather than very cold outside, you're doing further harm to it to discharge it even lower to get the caps charged to do the jump start. Maybe that is all you need to not be stranded, heck drive straight to a walmart open 24/7 and buy a battery there... even if their automotive dept is closed, I've been able to pull a battery off the shelf and checkout at a normal front register lane.
You could bring a long a separate battery to charge up the capacitors on one of these, for example a cordless tool battery or whatever, but you're going to have the tedious process of holding the cables to the battery terminals for minutes (length depends on the design of the product you choose) to get enough charge in it, and keep repeating doing this if the engine does not start on the first attempt so you have drained the capacitors and are effectively starting over.
I'd rather have a plain old 12V lead acid battery and a set of jumper cables, or if I suspected my battery was going bad, to just go ahead and replace it. On the other hand, I'd rather store one of these capacitor based jump starters in the vehicle than one of those dodgy Chinese Li-Ion jump packs. I don't trust generic Li-Ion powered products in a hot car unattended, too much of a fire risk but hey it's your vehicle so you can make that gamble.
Keep in mind that if you do want a capacitor based jump starter, you can make a better one yourself for lower cost than the example you linked but of course it will be larger, partly due to less integration and mostly due to larger supercaps in it.