How does Amazon maintain its dominance in the e-commerce industry?

At the simplest level, it is by being ruthlessly customer-focused.

But there are a lot of moving parts within that.

They most definitely have "first mover" advantage; it was Amazon and eBay that got the ball rolling in terms of e-commerce marketplaces.
They have massive advantages of scale, and are ruthless in using it to drive down their cost prices - whether it's warehouse space (where they offer to create a lot of local jobs, but in return demand massive tax exemptions, non-unionisation etc) or buying products from manufacturers. They also use it on occasion to buy up or drive out competition.
They gather and use very effectively huge amounts of data.
Marketplace sellers are a key part of their offering. They can demand levels of customer service that they themselves can't provide (good for the buyers !). They push sellers to drive prices down (for example in the niche I sell in, Amazon takes 15% of each sale in fees, sellers are typically taking margins in the 1-5% range). The inventory is funded by the sellers, and not on Amazon's accounts or depreciated for slow sellers. Most importantly of all, they gather vast amounts of data about what sells at what cost and selling price (and for top sellers will buy direct from manufacturers themselves and undercut their own marketplace sellers).
They control the vertical from top to bottom; AWS (Amazon Web Services) provides their servers, data storage and analysis. They control warehousing and distribution for their own products, and for their FBA service (where sellers pay to have Amazon store and distribute for them), they handle all customer interactions, provide support (by AI) to both buyers and marketplace sellers, and control the checkout process.
As a global corporation, they can move profit from unit to unit until it's in the most favourable tax jurisdiction. Amazon pays lots of local employment-related taxes, but very little corporation tax. It helps to have a GDP greater than many of the countries they are domiciled in !

So all in all, Amazon have got a lot of things right, but are totally ruthless in maintaining control and eliminating competition. It is a very disruptive business model which can be good for buyers but at the expense of smaller more local businesses.