I think they probably mean empathy for users on slow Internet connections rather than for fellow staff. Basically making you test your software on a slow connection once a week.
More tech companies should do this, and they should do more of it. On Empathy Days, iOS/Android software engineers should have to "live on" 6 year old phones, and desktop software developers should have to use laptops with 8GB RAM and 15" screens as their daily drivers. And Internet throttling should both reduce bandwidth and introduce random latencies and connection drops.
Too many developers just assume their users are on this year's phones and supercomputer specced desktops with three 4K 27 inch monitors and write their software to perform well on those systems.
