How do I walk without a right mouse button?

From a quick Google search, it appears that holding Control while clicking to simulate a right click; this should hopefully allow you to walk and hence play the game.

If that ends up being inconvenient, there are a couple other options you could try:
1. Try re-mapping the mouse buttons or something; I don't know if that can be done in DOSBox or in some other way.
2. Get a mouse that has two (or more) buttons and use that instead of your Apple mouse.

Apple Magic Mouse does have right-click, it's just not enabled by default. Go to: System Preferences > Mouse > Enable Secondary Click (exact procedure will vary by particular OS, but you can easily google it). Unfortunately, you still can't right-click and left-click simultaneously, so for that you'd still need a different mouse.