Question Galeros:
(please understand I'm using an extreme example for understanding, not for sarcasm)
If WotC sold D&D to me and I released 5th edition, which was the following:
1. It only has Dragons as pcs or monsters/npcs.
2. Each pc creates a dungeon in which to place its hoard.
3. It is player vs player (with some NPC dragons thrown in to spice things up).
4. It is called Dungeons and Dragons.
5. There is no other game called Dungeons and Dragons (apart from the prior editions)
Would my game be Dungeons and Dragons to you?
Edit: this makes me think of the line: "A rose by any other name would smell as sweet." but want to change it to "The name of a rose on any other flower would still be a rose." And now I'm not sure if I'm making any sense.
I'm not galeros but I will answer. Yes, it would be D&D.
To me to make it the D&D RPG it has to have two attributes:
1. It's a roleplaying game. (Duh)
2. The name Dungeons and Dragons.
Those two things make it The D&D RPG. To me, it's like a car model. I have a Scion XA, after the XA was released, they came out with the XB, which looks radically different. It's still a Scion. Conversely, Scions are made by toyota- They even have some toyota standard oparts, but they aren't a toyota. They're Scions.
Now, if you're question is Does this new edition of D&D capture the same play "feel" that the D&D RPG has historically offered: Well thats quite subjective, and I think that's why a lot of people get hung up on how you define D&D. (In my opinion, it very much does, and even more so then the previous edition. Your opinion may differ.)
As for 3pp games- sure they might offer a similar experience as D&D, or even be based off of the same rules set as a certain edition of D&D, but they're still not D&D, anymore then a car from Ford that offers a similar driving experience to a Toyota is a Toyota.
You might enjoy one as your favored fantasy RPG rules set, but you're not playing D&D. You're playing a fantasy RPG based off of D&D, known as "Whatever 3pp name it has."