Remember that your video is in addition to your application. Your application is where it all happens, and your video is giving you a chance to shine. But that's not to say just because you aren't a native English speaker that you won't get funded.
And if you think that you aren't a good speaker, then you might have missed the point on the video, you aren't suposed to speak like it's a talk, it should be a really informal introduction of what it is you are working on. You cannot stress the informality enough.
Just relax and talk into the camera like your chatting with your best friend. Being relaxed and being able to explain your idea shows that you understand your product really well, because people who have to work really hard come off as being unnatural and appear to have slower recall times as if they don't know what they are talking about. Robotics in talks is just bad.
For example, if you live in the same area but you don't even manage to gather and shoot a one minute matter-of-fact video that explicitly asks to avoid wasting time on it, then it'll be hard to believe that that team will be able to survive the pressure of a startup in its first couple of years.
Also, I think that in a startup environment you have to be ready sometimes to just quickly do things, and the video is a way to show that you don't need to invest three days scripting it and shooting it, but just half an hour making sure your words are audible and such.
What other startups say doesn't really matter. Startups don't have to try to guess how successful 1000 teams may be. YC has to.
Of course it can be gamed pretty easily so it isn't that much of an indicator. I wouldn't imagine PG has ever denied at least an interview on the basis of a bad video but he will have to clarify that.
I'm sure he mentioned that the video is only watched after the rest of the application has been read.
The video is a great place to show off your founders, your idea, and your passion for what you're doing. Having perfect English doesn't matter as much as communicating your idea and why you're a team they'd want to back.