Being able to cue and using sync aren’t really related and from the photo it isn’t possible to tell exactly how he has the equipment mapped, but in theory, if you wanted to manually beatmix with that setup you could map some of the line faders on the mixer to double as pitch controllers, or use some of the parameter dials on the midi strip. I suspect with a really intensive mapping job, you would have access to more than enough buttons and dials on that mixer to run an entire show without any additional controls.
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