Hello, I was wondering why when I was looking for a game by name inside the site I didn't got any results, but when I googled the game name it showed me a link that brings me back here at itch.io

How come the game is here but don't shows unless you search it outside the site ?

The game in question is Nightmare Knight, here are some images first I searched by name the y even copied the name just as it appears in the link that works and the game just don't pops if searched inside the site. 

And yes I did scrolled down till the end of the list for each search.

It's because of the indexing system. You can read the official Itch documentation here:

https://itch.io/docs/creators/getting-indexed

Long story short, not every game published on Itch is indexed by the internal search engine, it's that simple.

Also it looks like an adult game from your screenshot. You have to enable NSFW mode in your account settings before they'll show up.