Bezos still needs to focus on actually delivering the value that the world has priced into the expectations of his company. He can't just retire and collect income off of an existing machine like Gates.
Because Amazons stock price is valued strongly based on future potential. For Bezos to cash out now and do philanthropy, without a very strong replacement to realize Amazons potential, shares would fall 50% effectively halving Bezos' worth.
Regarding your second question, it is actually a similar scenario to when Gates left Microsoft. Right before Gates left, Microsoft was at one of the highest peak values, $58, almost it's Market cap today if you account for inflation, and a year after Gates left the stock had plummeted to $24 a share. Many would propose that Bezos leaving would actually be more detrimental, as Microsoft at the time was not a growth stock, but a well established money printing machine, while Amazon stock is still banking on future potential.
All shares are valued solely based on their future potential (cash flows). It matters not a whit what you did in the past, if your future is bleak, you share price will reduce to under book value
Bezos net worth is almost entirely Amazon stock, which is a growth stock.
Gates net worth is almost entirely cash (tens of billions in cash?) and other investments (there's like a holding/investment company that's actually just Gates).
More than most companies, Amazon seems like it's actually worth what people say it is. It's the world's largest e-retailer, with a huge percentage of happy customers (due to their great customer service), with a booming membership program, making strides into local deliveries (Whole Foods), with the largest cloud computing infrastructure in the World.
Much better in my opinion than Apple, that is almost solely valued off of a popular phone that the majority of users could replace with a phone 20% of the cost and be just as happy.
How is Bezos' situation different than Gates?
e: to clarify my second question: How is Bezos' situation different than Gates' when Gates left Microsoft.