There is no streaming API for GitHub. I doubt that they have plans to add one to be frank.
Your initial request may receive the last 30 events, and then poll the ETag header of this request for updates. You need to authenticate (somehow, not necessarily with the application) in order for it to work. Given that each request must come from a different IP address, I would jeopardize that speed limits will not apply globally to all visitors, regardless of who they authenticate with. This, however, would be a great question for the GitHub API support team.
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