It is a 2-speed. So it is a bit of a trashy comparison: He lacks shorter gears, he lacks in-between gears and he spins out at the end of the race in the highest gear. This has absolutely nothing to do with riding a folding bike but with choosing a folder with an unnecessarily limited gear range for the challenge. Basically they cement the false prejucides towards folding bikes in this video.
What they also don't say (but you can derivate it):
• In comparison to his own hill racer the Brompton has about 5+kg of weight penalty
• it has a way more limited gearing top as well as bottom (but we don't know how much)
• on the 2-speed Brompton which is completely new to him he does ride the hill just 2mins slower than on his own hill racer
So not too bad I'd say - though the race and the comparison is misleading and of no use at all. It is just a spectacle for creating clicks, not for any serious knowledge gain.
Can a folder climb? of course it can. You have to bear in mind that you can't pull up on the bars, and it doesn't respond well to standing on the pedals and heaving on the bars either. I don't have a Brompton but I bought a budget folder a few years ago and adapted it with lower gearing to cope with route to work. I changed it from a 6 speed to a 7 speed with Megarange bottom sprocket. It's mostly fairly level, but has some short sharp climbs either side of the river which I had to cross in both directions.
You just need to adapt your technique. The rear triangle is the strongest part of the bike and so as long as you can discipline yourself to remaining in the saddle and using your lower body to propel yourself up the hilly bits it will transmit the power fine. You need to pedal smoothly even if you're not necessarily a spinner.
By all means lean forward over the bars to keep some weight over the front wheel on the steepest bits but until you reach a gradient that makes steering difficult, I find my folder climbs OK. If you've got the gears, you can climb almost anything on almost anything. Going downhill fast on those small wheels -now that's another matter!
This unexpectedly benefited me a few years later when I got into riding recumbents. The same old predjudice -folders can't climb, recumbents can't climb, (insert name here) can't climb! My original recumbent couldn't be more different from my folder. The folder perched you waay above the wheels, you might get a nose bleed just thinking about it, and the wheelbase looked ridiculously short, though that was just an illusion.
My LWB recumbent looks like it ate my folder for breakfast without noticing. Loong wheelbase, low seat, yet to get up hills here we are again. Can't use your body weight on the pedals, can't pull up on the bars. Just use your legs and the appropriate gearing. Somehow, it just does it.
When I do get out on the folder, it's always a pleasant surprise how nice, if slightly strange, it is to ride. It's not fast, being a bit low geared, but just climbs everything you put in front of it with no fuss.