Does GOG take that long to check? Or is it up to the developer?

A lot of A, a little of B.

And who says it was an earthly reason to begin with?

Was it perhaps the engine? Does the check take longer if you have your own engine (instead of Unitiy for example)?

No. If at all, then the size would be a aspect, not the engine. Many games have their own engine and most have no problems.

It's safe to assume that the delay had no technical reasons, it worked in two other stores, so why not even announce it on GOG.
We will most likely never know the truth, but it most likely was some marketing issue. One speculation was that they wanted to force Steam sales first, so they would get a higher cut ... no one knows for certain.
But the wait is over now anyway.