Most browsers support image maps, so it should work all right with Safari browser. Unfortunately, you cannot use variables with strict html.
This limitation can be worked around with careful design, not unlike the designs used in choose your own adventure (cyoa) books. If you want to go crazy, you can use ...10100101010 string at the end of page urls, to carry the variable values from page to page.
Here's an example of what can be done with html and image maps. Try to play through it, it's not that tough a game, and pay attention how solving the mystery is handled at the Chief's office with multiple questions, instead of variables.
Good game, in fact.
Remember, you can use "view source" from your browser to see how each page of the game is done. I think the author used a web development tool called "Web studio" for making the game, but other tools or just good old Notepad are surely good enough for the purpose.
Here's another take on the html-only game format:
So, many things can be done.