idk why but the itch.io i have on my Laptop is extremly different. First I have a Icon on my screen, second when i want to install a Game bar pops under it out and says "install". Then i just need to wait until its says play and then i can play it. On my PC there is no such a bar, i need to download it and then open it in my Downloads (on the Pc and not on itch.io self) and thats mostly dont working. Plus I can only open it thought the Browser unlike at my Laptop. At the beginn its only worked on the Laptop like at the PC now but I have no clue how I change it. Also its in German on my Laptop, so has this something to do with the language? Or the Icon? Would be great if somebody can explain this to me.

Your laptop probably has the Itch.io client software (or app as it’s called). It’s freely downloadable, but both methods should work.

If something works with the app but doesn’t work through the browser then you’re doing something wrong, because the app basically does the same thing.