You can take exception all you want, but you've inadvertently just exposed a weakness. The point of server grade ethernet chipsets is that they're optimized for coping with a high number of simultaneous streams, including TCP offload, interrupt coalescing, virtual function support, multiple queues, and doing this with relatively low latency.
Web browsing tends to be a small handful of simultaneous streams, a task which does not necessarily require assistance in the form of dedicated silicon for TCP offload or most of those other "server" features.
Competitive gaming tends to be oriented towards a low latency single stream of packets, which is relatively easy to deal with. You do not need really need hardware assistance for this, which is why the Realteks have been "very solid" in that environment.
Both of these are substantially easier workloads for the ethernet chipset than many server workloads, where server chipsets can be asked to support hundreds or thousands of parallel streams at once.
It used to be that web browsing only consisted of two or three simultaneous TCP streams, but over time we have seen this grow to a somewhat larger number. It's still not hundreds or thousands, though. As the speed of Internet connections increases, and the complexity of things that we run in the background on a PC increases, the limits of the Realtek ethernet chipsets get closer and closer. At some point, you're going to feel that today's Realtek ethernet chipset is not performing well, just as you would probably feel that yesteryear's 10/100 Realteks really sucked if you tried to use them today, even if you only needed less than 100Mbps.