Not to come off like a jerk here, but man there is a lot of stuff in that video that is just plain wrong. First the trem claw shouldn't be tightened that far, especially with no strings on there to begin with. And the soldering job is cringe worthy. I don't even want to start going over what all they did wrong there for fear of sounding like a solder nazi.
I can't speak for the kits from experience, but the only thing that this thing has in common with a Jem is the shape. The hardware is cheap, cheap, cheap. You can look at the back of the pickups in that strat and tell that they use the same type you'd find in a cheap chinese guitar from about 10 years ago...I don't even think that they use those type anymore. Its a ceramic bar magnet that touches all the pole pieces. They work, but they sure don't have that 'vintage tonez'.
The body is basswood which I believe means whatever the hell they want it to mean. I know that my Axis has a basswood body and I love it; probably my favorite guitar, but it's also got top flight hardware and nice pickups in it. My heart tells me that it would suck, but my head tells me that as long as all the holes and crap are in the right place that it'd probably be fine. You could always go out and get a better tremolo and better pickups. That kind of stuff is easy, but it starts eating into the savings really quickly.
Out of everything in that kit that can't be easily swapped out if it's dodgy is the neck. I doubt that its going to be dressed very well and it's probably going to need a bit of work. If you can do a fret level yourself I wouldn't be surprised if you could make it into a really nice playing guitar, but I'd be willing to bet almost anything that it won't approach an actual Jem's feel and action and whatever even with a top flight tech massaging it. I just think that it will have a high or low spot after its under tension and that the wood is going to move. I base that purely on gut feeling, I could be completely wrong. But I doubt it.
It does look like it'd be fun to put together and if you have always wanted to do something like this then it's a great way to get into it, but don't expect to end up with a fantastic instrument after its done. Has less to do with you than it does the materials itself.