I don't have Amazon Prime (nor am I in the US) yet use Aliexpress perfectly fine on my mobile phone without using an app. Frankly, I don't understand how the two is related at all?
Both are web stores. Both have websites AND apps.
They are compared / contrasted. Nobody is saying one is concretely related to the other.
AliExpress won't allow me to open most pages in the account section on my iPhone. Instead I get a page telling me to install the app.
While browsing, there are also popups offering the app approximately every third link I click. Some of them are telling me to install the app.
Unless the situation has changed recently, it's not perfectly fine, it is unusable on purpose.