The English example above isn't a "menu" - it's a numbered list of arbitrary foods arranged alphabetically. It wouldn't make sense as a "menu" in a restaurant even in English.
A customer who wants a sandwich would likely be confused/frustrated trying to find all the various sandwich options scattered alphabetically across the page.
Since people don't tend to choose food by name, but first by meal or category, a "menu" needs further organization.
- specials, breakfast, lunch, dinner, dessert, drinks
- specials, appetizer, salads, entree, dessert, drinks
You'll find a similar structure in many menus regardless of the language or style of cuisine.
Chinese menus (in the U.S., China, and Taiwan in my experience) can be a bit different in that they tend to be organized by food content: appetizers, soups, noodles, rice dishes, chicken, beef, seafood, vegetarian, house specials, drinks (not necessarily in that order).
Within those categories, the specific style or type of cooking tends to be the next sub-category.
- Chicken Fried Rice
- Shrimp Fried Rice
- Pork Fried Rice
- Happy Family/Combo Fried Rice
- Steamed Rice
- Hunan Chicken in some sauce
- Szechuan Chicken in another type of sauce
- Gen Tso's Chicken in a 3rd type of sauce
- BBQ chicken (no sauce)
- Stir-fried chicken w/veggies
- Stir-fried chicken w/different veggies
This method of sub-categorizing helps to group related styles of dishes, but since the key component of the dish only comes at the end of the name, you couldn't really "alphabetize" it anyway.
There's really no discernible "order" beyond that as far as the name is concerned - not by character complexity, pronunciation, or by spoken tone. You could at that point order by price, popularity, or some other attribute.
If you really want to try, then you would use "radicals" or parts of characters that combine to make up more complex ones ... but considering that this doesn't seem to be the case in existing Chinese menus, I don't think it'd be understood or worth the effort.
... And after all that, I'm wondering whether you really wanted a "food" menu, or you're talking about how to structure a UI or navigation menu in Chinese. Actually, I think the same principles would apply - organization & sub-categories. Put the most important/frequently used items in more prominent positions.