Wikipedia states that there was National Treasure edition that included 9 more DLCs than Game of the Century Edition. In the GOG description there are only 5 DLC and I don't see Enter the Dominatrix and How the Sints Save Christmas that are listed in Steam. So I became doubtful are there really all DLCs included or "meh... there is a lot so let's call it complete collection"?

And by 5 mentioned in the description, you mean this?
The American (Fever) Dream – Play as the President of the United States in a story that spans countries, space, and time. Saints Row IV is to Saints Row: The Third what Saints Row: The Third is to Do The Right Thing. You’re not ready.

Super Hero-in-Chief – Leap over buildings. Kill people with your mind. Run through tanks. Those are some of the most mundane powers you will wield in your quest to stop an alien menace hell-bent on destroying the Earth.

Alien Toys of Destruction – Wield an impressive array of alien vehicles and weapons… FOR SCIENCE!

Custom Weapons, Custom Mayhem – You’ve customized your character. You’ve customized your clothes. Now you can complete the look with our all new weapon customization system. Turn traditional weapons into exotic conversation pieces!

Dynamic Duo – Seamless drop-in, drop-out co-op, a Saints Row standard, improved. The only thing better than one malicious super-powered President is two.

Yeah. Aren't those DLCs? I've never played this game and really don't know much about it.

Excluding the season pass, there's 25 pieces of DLC on sale through Steam.

This site has an itemized list of what was included in the National Treasure edition (sadly it does not sort the skins and outfits into what packs they appeared in) - http://www.playstationlifestyle.net/2014/06/24/saints-row-iv-national-treasure-edition-arrives-next-month-is-packed-with-dlc/

As to what's in the Game of the Century release, this covers it - http://saintsrow.wikia.com/wiki/Saints_Row_IV#DLC

It's as complete as it's ever likely to be (I doubt they bother to patch in the Re-Elected skins or the TF2 weapon skins that were a pre-order bonus back when the vanilla game was nearing release).

No, that's just a description of the base game.

No, they aren't. They are just the game's bullet points.
Edit: Ninja'd.

Thanks guys. I was mislead by the phrase "And this edition even includes all available DLC!" before the list of features.

From what I read in links above there are no quests or some meaningful parts of the game missing, only skins. Or am I wrong again?

Just hate all this DLC crap. Just release one expansion instead of dozens of little pieces.

No, you've got it correct. All the story-based DLC is in there.

Check the little asterisk in the list on the wikia and you get taken to this:

http://marketplace.xbox.com/en-US/Product/Voyeur-Pack-I/5b784c2a-e221-407c-ace2-0038138f09fa

with a description of:

"This free pack will help keep your co-op game rolling if your partner has downloaded additional DLC content. This free pack does not allow you to have access to use any DLC content, but allows for full compatibility in a co-operative game."

It seems to repeat across the board for all iterations of it and (apparently) the fourth Voyeur pack would give access to the free "Thank You Pack" DLC to console players.

It's odd that the Child's Play Pack isn't included though. Not that it's the end of the world without it there or anything.

The Child's Play Pack is present in the game.

Here is the link to the steam version

http://store.steampowered.com/sub/47804/

It shows more dlcs than the GOG version

Looks like the same 25 (excluding the season pass, which is irrelevant given that all the content it provided is already included and for some reason both the vanilla game & the Game of the Century version of it as two items) as previously mentioned.

What K1ller said. Nearly all DLCs unlock after you leave and re-enter the Simulation for the first time (And it where so many I almost started to get bored to click them away :P) and some (like How the Saints saved Christmas) after a storymission.