The gameFirst, HOGs work really well as casual relaxing games. Everybody gets it that different genres of movies elicit different emotions - and the same is true about games. HOG's strength are at creating relaxed time for the player, in artistically interesting world with a bit of storytelling - but if you miss that and try to make them very challenging (something that works very well in many other genres) the player will likely find that frustrating. So throw away timers, scores, and such nonsense. Hints should recharge, not be finite (they don't have to recharge fast). Some games have hardcore mode you can choose from the menu - that's OK, just make casual mode available as well.
The best way to distinguish your game from all others is in distinct art style - and HOGs' diversity stands in contrast to mainstream gaming's obsession with a handful of trends like the infamous brown and grey color palette. 2D art styles tend to look a lot better and immerse in the world more effectively. Some HOGs try "realistic" 3D, and that usually just falls flat.
By the way - in the Extra Credit video the guys are surprised by protagonist being generally female. I've never really noticed that as being in any way unusual, since in most mainstream games other than military shooters and JRPGs you can choose to play a female character if you want to, and as far as I remember the HOGs I played, there were female protagonists in maybe a bit over half of them - it was closer to balanced than to overwhelmingly female.
If you really need walls of text, they should be spoken, but generally avoid walls of text and keep cutscene to gameplay ratio within reason. Distinct art style works a lot better at establishing the world than walls of text.
The player is not your enemy. This is true in all games (I'm speaking about you Paradox and your damn comets!), but especially so in such casual games. Don't hide barely visible slightly darker grey rectangle on grey backgrounds (not too often at least), hide instructions, or force the player to try every single item on every single location in order to proceed because your preferred solution makes no logical sense. The last problem is not new to the genre - it plagued 80s' adventure games even more. Do some playtesting and if players keep trying to carry water in a bucket and you want them to use a kettle instead at least include some explanation on why that doesn't work ("Sorry, the bucket leaks").
Puzzle sections need a restart button. Hopefully you came up with a new kind of puzzle, so the player might want to experiment with it a bit before trying to solve it properly - but then the puzzle might be even more messed than when it started. Just add restart buttons to all of them in case that happens. And obviously there should some instructions, and a skip button (with suitably long time before it becomes active).
There should obviously be some hidden object sections. Try to come up with a bit of variety. Different games have tried so many twists on this that by now you can just pick and choose a few from other games.
Nothing in the game should ever be based on reflexes. No irreversible decisions screwing the player should be possible ever - there's a reason these games don't have quicksave of any kind.
It's perfectly fine to have some kinds of achievements like for completing a chapter in under an hour, or finding some optional and possibly difficult to find items - most players won't really care, but some might.
And that's it for today. Enjoy the gaming. If you're completely new to the genre I'd recommend starting with Mortimer Beckett series - that's what got me into the genre as well few years ago - but there's a ton of other great games out there. (feel free to post your recommendations in the comments)