(Note: I just want to discuss the legal stuff, no investment in SF or what Sega are doing here, also I am not a lawyer, just have some experience here)
A few people have mentioned fair use as a defense against claims of copyright infringement, but my understanding is that this doesn't usually hold water. For one thing, fair use isn't defined the same way in every country, and the definition from the country of origin of the IP holder might take precedent. Japan in particular doesn't really have robust legislation supporting fair use like the oft-cited 17 USC 107 section.
Also, fair use isn't just something you can claim like a get-out-of-jail-free card. You need to make proper attribution and be using a limited portion of the original work, like quoting text in a book review or using a short clip from a film in a video work discussing cinematography techniques. Which part you use also matters: there was a famous case of (I think) a newspaper book review quoting a very short part of a famous person's autobiography but as it was one of the juiciest revelations in the book, the publisher sued and won the case that it wasn't fair use because it significantly damaged the commercial viability of the original book. In other words, they quoted the part that was demonstrably one of the main reasons people might have bought the book. You can see how this can start to apply to Let's Play-ing an entire game on YouTube: it's at the discretion of a particular developer or publisher to decide if showing their game off like that is of value to them.
It doesn't matter whether or not you make money from your video, or whether you think you're giving them free publicity, as the copyright holder is entitled to control how their work is used and may not want your particular brand of publicity. (Edit: personally, I think they should leave small-time users who are clearly enamoured with a game alone...)
Anyway, if I'm completely wrong about anything then it would be great to hear from someone more knowledgeable!