No, I don't think I've seen that being claimed. It has been claimed that they have used their anticompetitive practices against others. Having Walmart as a competitor doesn't mean that they don't have a dominant market position with power to abuse at their disposal.
Conversely what's Amazon's share of physical detail? (Preferably excluding whole foods since that's an arguably different business to selling cheap electronics and other junk)
It's as if the two companies operate in... different spheres!
That is plenty large enough of a chunk to have significant economic influence. As a reference point, it's about the same percent marketshare OPEC has on the oil market.
Even though the topics are frequently discussed together, anticompetitive behavior is something different than being a monopoly and one does not require the other.
Someone who owned 36% of all the land in the United States would certainly be considered to 'controlling a large share of real estate'.
In the case of Amazon, it's even worse, because despite a 'mere' 36% market share, there is a lot of evidence that they have market-moving pricing power.
They generally exercise it by restricting the prices sellers can charge in other stores. This happens to almost all sellers on Amazon.