How I learned kesa gatame in judo is almost identical to how Steven Koepfer shows it. Both legs straight – one at nine o’clock and one at twelve o’clock so that you have dispersed weight and a bolster to stop bridging in either direction or being able to get leverage to take you backwards. Mike was showing for no gi a variation that looks more similar to how Joel Bane demonstrates – one jack leg, one drive leg. However, we were still doing head-and-arm, not kuzure kesa.
Mike’s variation is a tremendous amount of pressure. If you’re not used to being pinned by bigger guys, if you don’t know how to control your breathing a bit, before he even pulls up on the head for the added leverage into the chest you may feel the need to tap just from chest pressure. Using one leg to drive in and one leg to lift your hips off of the ground makes that pressure. However, doing so means that both legs are pushing your body backwards. Without the gi, that doesn’t really mean anything. It just means you’re getting free pressure. They’d have to get the far (non-trapped) arm in front of your face/body to push you backwards in no gi. With the gi, it means they can grab the lapel and do the sit-up escape.
Building pressure with the variation I’m used to necessitates a strong pull on the arm and sinking your hips forward. Your hips should still be off the ground, but subtly low; the lower they are, the most weight uke is holding. Winding in and driving your hips forward still won’t generate as much pressure as the jack/drive system from the other though.
Typically, what we do in no gi is equally valid in gi, but not vice-versa. An armbar, a choke, even a shot you would use in no gi can be used in gi with minimal modification. But a lapel choke, a sleeve throw, or a grip relying on the jacket won’t work in no gi. In this case, the gi version works in both contexts; it’s just potentially suboptimal in no gi given that there’s a better way to generate force there.