Not exactly. The press system simply gives reviewers free copies of games, but unless if the developer puts an email address of some form of social media in their profile, there is no way to directly contact them for various reasons. Eg. To give feedback, or to ask if they would prefer a spoiler free review, or if a full let's play is ok, etc.
Legally you can make the video however you want. The type of video you make should depend on the viewbase you have. If they like spoiler free, do spoiler free. If they like full Lets Plays, do that.
We can't limit what you show in your videos and you don't need our permission. If you're wanting to just be nice and ask anyways, most developers have a Twitter listed on their profile.
In honesty, I doubt many developers even check Itchio weekly, so even if a DM system was implemented, you might not hear from them for awhile whereas just sending them a tweet will be much quicker. I myself only check Itch so often because my primary project is an asset that integrates Itch App and Unity haha.
I see where your coming from, but your saying that I'm allowed to make the video however I want simply isn't true. That all depends on how you interpret the laws around it. Yes, so long as my video follows the conditions set by fair use I should be make the video however I want within those restraints, but that law can be interpreted so many different ways, and the precedence court cases as of so far have sided with the creator of the original content, not with the creator of the derivative work, meaning that even if my video technically fell into fair use, the developer could still have it taken down if they want because it's their game. It is because of this that I still contact the developer of every game before I use it to be sure.
Also, yes I agree that it makes a lot more sense to contact developers external to itch. I'm saying this should be a thing anyway because of the developers that don't have a twitter, or email, or any form of contact within their profile, making it impossible to reach them.