Not enough time to do a real comparison, but Uber feels a lot bigger than all of the mid-sized startups which dominated the dot-com landscape. They are a lot bigger than Webvan was (22,000 vs. 3,500 employees) not to mention Netscape (2,500 employees at its peak); Webvan and Netscape were the most famous big dot-com flops.
Thanks for the data point. It's helpful, but I'd be worried about extrapolating too much from one outsized data point.
For one thing, BLS stats say that computer programming has grown from 528k to 1666k from 1999 - 2018 (the broad category of Computer and Mathematical Operations went from 2620k to 4384k). For another, just looking at the largest company only works if the distribution is similar.