I think its the other way ard, they contact you if they feel the catchment area of your yourtube acct is credible.
Not sure what you're asking exactly. Like -- how would you, yourself, get into the game of reviewing figures? Well first off ... You would start off by buying your own figures. You would then need to set up a YouTube channel. "Advertise" (if this is allowed) subtly and without making yourself look silly by spamming threads, and see if others would subscribe/watch your videos. If you have a decent camera, a steady non-nervousy voice and you begin to gain some popularity; I would then and only then attempt to contact a company and try to get a figure for review. If you are an unknown I wouldn't even waste my time attempting to contact anyone.
No problem! I didn't mean any discouragement by the way - you could be an awesome reviewer. Try reviewing something you currently own, and see if you get any subscribers/views and whatnot. Good luck
Pretty much this. It's the same as game developers sending copies to a gaming site for review. They're saying "A lot of people look to your views and listen to what you say. Here's this thing, will you tell people about it?"
At least a few of the 3rd parties have personal email addresses that they share with the vendors and reviewers that they work with. If you know the right people, someone will probably be willing to share one of the addresses with you. Then there's always facebook and PMs on sites like these.