I haven't thought of a precise way to measure this - it's largely based on the "feel" of the responsiveness. Another example is shown here:
https://www.youtube.com/watch?v=A-xZXSa3zck
There are plenty of other minor discussions on this scattered around the net, but most seem content to say "yeah, BizHawk has a lot of input delay, but RetroArch/snes9x/other feel pretty good. Use those instead." That's part of the reason I wanted to bring this up - I swear there was a note or comment on one of the BizHawk releases that due to a change in how rendering was handled, there was added delay between user input and registered input. My memory says it was at the 2.0 release, but I haven't been able to find any comments or notes confirming that. Knowing where the cutoff is can at least point folks to something a bit more playable.
There are other mechanisms that some emulators try that reduce this further - RetroArch has a sort of read-ahead mode that calculates future frames and applies the input there - but I think there are probably some tweaks that can have an impact on playability in BizHawk without going to that level of complexity.