I'm trying to understand the concept. Does the color of the checkboard matters?
I'm confused
No, and you will have to show the puzzle/game/setup from beginning and tell us exactly what moves you made.
The screen shots you've provided do not show enough information to tell you what happened.
You basically cannot place an attacking piece next to the opponent King if that piece is NOT protected.
Typically a Queen + King vs King mate occurs by 1st - backing the lone King to the edge of the board - then 2nd - with the King 2 squares away giving check with the Queen and mate where the lone King has no escape square. The Queen must either be checking from a distance OR is next to the lone King with your King defending the Queen.
When I played a few times, I noticed I was checkmate when the Queen piece sat next to my King piece. In this computer (opponent) game, it didn't checkmate. Why is that?

Here is the photo. I put the two photos together, so you can see it.