Am I 'legally' within my rights to record my game play, and upload to my YouTube Channel? Are there 'copyright laws' being broken here? If so, is there anyone from 7 Days To Die, I can contact and 'Ask for Permission'.
In general, unless the game publisher has explicitly given you permission, the answer is (in I would wager many/most) jurisdictions:
1) Yes, you are legally allowed to record (for own use).
2) Yes you are allowed to upload to anywhere (for own use).
3) No, you're NOT allowed to give OTHERS access to the footage. Which makes YouTube pointless if you just keep it private. But you can use it as a video storage site just like dropbox. As soon as you share the video content, you're distributing it which normally is license violation and often a crime.
4) Yes you normally violate a bunch of copyright laws, and likely your terms of use not only for the game, but YouTube as well which prohibits sharing copyrighted material.
That said, those don't really help you, as in MOST (not all!) cases Game Publishers are very happy when people play, record, and share their gameplay. Some have been known to make explicit licenses for it available (on their website). Most simply leave it unsaid in order to not open up the legal box of a poorly worded license, leaving open in the future to making one should there be a need. Since more views means more sales (normally) it's a win win. However, mutual benefit doesn't make it legal as such. I know at least one Early Access game I have, that I can not cover as the publisher specifically disallows it under penalty, so I simply don't record or play it until they relax their use license.
For 7 Days to Die content, TFP have been very supportive, and you'll also see mods, Roland especially, who've had threads linking to guides and footage, their twitter account have pushed out info on videos, streams etc, to support the community.
You often hear people speak about fair use, and such. However most videos on youtube using copyrighted material would never pass the criteria for fair use. It's a huge topic of its own, interesting to read for those who are so inclined, but more important is really "will I get into trouble for it?" is sometimes more useful. Unless you get a copyright strike, nothing is likely to ever happen

And copyright strikes can happen regardless of whether you have a license or not, whether it's copyrighted or not, so has little connection to the legality. I would wager the risk of getting legally in trouble (ie, sued) by a publisher for making a video on YouTube is so small that it's unlikely to be an item to spend much time on
And for the record, I make YouTube videos of 7 Days to Die, and I stream it, and I love it!
https://youtube.com/vedui42