Is this game somehow connected to Observer
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no... butterfly is an extremely common word used in the phenomena of time travel where one action has a huge ass effect. Hence Jack was nicknamed butterfly cause we are an "anomaly" that caused a great calamity.
In short... yes, reading peoples minds can cause butterfly effects. So thats why this is called butterfly aswell.
If you mean the game released by Fouzi, than yes. The original Butterfly comes from the Happiness series. He is one of the most important characters in the games. This game is a remaster of his origin.
So basically, the Zero, the Butterfly and the CC you see in this game, are the same from the game Observer.