The pricing benefit really cannot be understated.
Amazon was 40% less than list for books -- which was a massive amount, even if you lived in Barnes & Noble markets (and B&N wasn't as pervasive in 1996/1997 as your average mall bookstore was), where there were similar markdowns.
And of course, you could get any book you wanted from Amazon.
And then Amazon very quickly moved into media like CDs and DVDs. I used to order DVDs from various online retailers in the late 1990s and although Amazon wasn't my go-to in 1999/2000 (there were plenty of startups that sold at ridiculous losses and coupons that 16 year old me took advantage of), I appreciated their selection -- not to mention the gift certificates.
I think a lot of us forget that Amazon wasn't the only big e-tailer in the late 90s, it's just the one that survived. There were lots and lots of bigger and smaller places that straight up went out of business after the .com crash, but Amazon, despite taking a massive beating, survived.
Price was a huge reason for its success -- but I agree with others who point out that Sears and other incumbents had a chance to take them on, if not on price, than on selection and speed, way earlier than they did.
Instead, many businesses chose to partner with Amazon (Borders, Toys R Us) for a time, to their ultimate detriment.