Although not a "new" form of advertising, influencer marketing seems to have a much more prominent role today with the rise of social media as well as the new media (as opposed to traditional media...CNN, NYTimes, USA Today, etc).
There is currently a wide range in regards to budgets and much of it is currently dictated by the influencer themselves.
Big brands (Fortune 500's) tend to still stick with known celebrities and work through agents. Alec Baldwin claimed to have made $15 Million for his series of Capital One ads.
Smaller brands tend to focus on smaller influencers...and big / small is determined by both the size of the following as well as the loyalty of that following.
For example, I recently worked with a small brand (~250k in revenue) that hired a small influencer (mommy blogger with about 100k followers) and it was a super successful engagement because although small, those followers were loyal...she was a trustworthy influencer. That brand paid a flat fee of $5k which yielded about $20k in sales.
More and more brands are looking into sponsoring streams but currently it is still only a small percentage of their budgets...generally no more than 5% of their overall marketing budget. As always there are situational exceptions and many companies use a multi-faceted approach (traditional ads, digital ads, influencer marketing, affiliate marketing, etc) but sponsoring streamers is still a very small part of their overall marketing strategy (if part of the strategy at all).