Hello
I'm not the developer, but you can do what the website implies by stating that iPhone can use PWA ( or a Progressive Web App )
I don't know if Safari has it ( I don't own an Iphone) but Chrome definitely does. Just open up your Tamagatchi on chrome and do these steps. I hope this helps! 
Inc3000
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A member registered May 10, 2020
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While I'm not a software developer I am an IT technician with a lot of hobbies
I really appreciate the work this developer has been doing on Tamaweb and when I saw your comment wondered if there was currently already a way to turn the web site into a Mac OS compatible Progressive web app. neither of the programs I found do this for free, so I turned to pake, a command line based Progressive web app generator that I've used to create PWAs for Windows. I grabbed the website icon and URL and input it into the tool and it gave me back the file I sent in the post above.
I have not been able to take screenshots or test it as I do not own a MAC, but I followed this tutorial for the tool Pake. You can feel free to make your own Tamaweb MAC OS PWA using this process at least until the developer can create an offical version.
https://github.com/tw93/Pake/blob/main/docs/github-actions-usage.md
I hope this helps!
hello this app should let you use Tamaweb on Mac OS
I acknowledge that you have no reason to trust a stranger from the internet so I'll reply with a full explanation below Tamaweb MAC OS PWA - Google Drive Link