The market responds to Trump's tantrums because it affects the potential of Amazon in the future.
Basically, if Trump threatens to take some action against Amazon that may hurt its value as a company by 10%, and investors believe there is a 50% chance of Trump following through with this threat, the investors will (theoretically) collectively lower the price of the stock by 5%.
A price on a stock market is determined wholly by future outlook, which a president's negative tweets can affect, hence why some companies with high earnings expectations in the distant future cough Tesla cough have ridiculously high price/earnings ratios on their shares.
Only companies making profits have P/E ratios, Tesla is still losing money so its P/E doesn't dictate its share price, only its projected future growth/sales.
P/E ratios don't tell the whole story, e.g. AMZN has a high P/E ratio because they aim for low profitability by reinvesting in growth, similar to Netflix who's still taking on debt to build out its inventory.
When a companies growth and revenue has stagnated their P/E ratio then becomes a strong indicator for market value / share price.
The part you omitted is how the long-term outlook currently priced into a lot of tech stocks (including AMZN) is far too optimistic and not accurately discounted relative to likelihood. Current prices aren't a function of rigorous analysis so much as pie-in-the-sky projections and too much capital floating around.
The efficient-market hypothesis basically asserts that if a price weren't a function of rigorous analysis, then there would be a sizable incentive to find and correctly analyze this stock, and trade appropriately to take advantage of the inefficiency until it no longer exists.
There could possibly be a more optimistic pricing in the markets if we factored in, just as a random example, that people are more timid to short rather than buy, as a short can easily result in a loss higher than the entire value of the position. An interesting read if you'd like to go down the rabbit-hole of that ideology would be anything on the concept of 'Adaptive Markets' by Andrew Lo. Rather than the common physics/maths-based approach to market behavior, it focuses on a more biological one, and thus includes these 'emotional inefficiencies' that may be present in market pricing.
Basically, if Trump threatens to take some action against Amazon that may hurt its value as a company by 10%, and investors believe there is a 50% chance of Trump following through with this threat, the investors will (theoretically) collectively lower the price of the stock by 5%.
A price on a stock market is determined wholly by future outlook, which a president's negative tweets can affect, hence why some companies with high earnings expectations in the distant future cough Tesla cough have ridiculously high price/earnings ratios on their shares.