I don't think they use haproxy (or at least they don't heavily rely on it). But once you start with properly scalable tools, you "just" need to have a high bandwidth and many machines, and everything becomes easy. Think about it for a second, put a 40 GbE NIC into an single-socket haproxy 1U pizza box, you get this for $800. Take 25 of these in a rack, connect this to an L3 switch doing ECMP and you have 1 Tbps of DDoS absorption capacity. For $16K. I know pretty well I'm oversimplifying the problem, but it always starts this way, and after this you adjust for various aspects (small packets, reflection using tools like PacketShield, TLS handshakes using more CPU cores, large connection counts using more RAM) and that's about all.

The heaviest and hardest to maintain features in these environments are the fat stuff that customers want (WAF, monitoring, UI, config versioning, etc). But basic protection is trivial if you can afford the bandwidth.