This website has some details + schematic for the ZVS induction heater oscillator, the listing you linked to is probably pretty closely based on it:
https://spaco.org/Blacksmithing/ZVSInductionHeater/1000WattZVSInductionHeaterNotes.htmYour biggest electrical concern with parts / kits from China is going to be fake power transistors. However, the power level you need for a vape is going to be pretty low, so you should have a lot of leeway. I expect anything sold as an assembled kit is going to work long enough to allow the seller to reject any return requests.
Also, based on your youtube I can not tell if you have a fuse. If not, add one! LiPo battery packs can source a large amount of power into a short and DIY power electronics have a tendency to go boom.