I tried both your games 'Ball Dodge' and 'World War Zoo'.
They both work as soon as I tap on the 'Launch' button. They instantly get into full screen for me.
That being said, 'World War Zoo' gives me the notice that it "may not run on my device, but I can try it anyway." I would assume this is the message supposed to appear if it is not set to 'Mobile Friendly'?
So... I am not sure why it does not work on your device. Do you have some stuff enabled in your device / mobile browser / itch.io settings?
I used Chrome to try it out. The phone is from... 2020? I do not believe I have enabled any peculiar settings about full screen, but I could be wrong.