You can lose grip on what is real without assuming it's a game though.Well for normal people, no. But Gungnir was already a psycho, and with his multiple lives and him thinking this life is a throwaway before he starts his "real" life, was enough to for him to convince himself that this reality is just a game.
This story utilizes the 101 reincarnated individuals to explore how different people cope with experiencing multiple lives/deaths. Some think of all of their lives as being one continued existence, some want to put the past behind them and live their new life to the fullest, and some completely lose grip on what is "real," etc.
Like he could have assumed it was a dream, an artificial world, maybe even one made for him as a sandbox, or that the ppl there are puppets of that god, or that it is any number of other "fake" world. But instead he decided on the thing that he had absolutely no basis to think it is (and all the reasons to think it isn't, whatwith literally just having met a god and had him reincarnate him into a world), a game made using overtech in his original world and no memories of actually wearing the hardware etc.?