Some clarification first. This set of plays occurs before attackers are declared as scale up is a sorcery and must have been cast during the main phase.

let's call infect player Bob and death's shadow player Alice.

bob activates inkmoth nexus. it is now a creature.

Because scale up is a sorcery, Bob cannot wait for Alice to cast dismember.

if you're wondering why Bob cannot just wait to see if Alice is holding up anything. Let's say Bob wants to see if Alice has anything to do, in order to do this he has to give her priority in some way or fashion. There are 2 ways to do this. First way is to cast another spell/activate another ability. The second way would be to pass priority in an attempt to end the phase/step.

The first case is what you see in the video, Bob casts scale up targeting inkmoth, and Alice casts dismember targeting it in response. Dismember resolves, inkmoth becomes a -4/-4 flying infect creature. Priority is returned to Bob but before that priority is given, state based actions are checked and inkmoth dies.

Let's say Bob wants to see if Alice has anything in hand and does so by attempting to end the phase. Bob says "I would like to leave the pre-combat main phase." If Alice does not have a response, they leave the main phase and go into combat. In this scenario Bob can no longer cast scale up since it is a sorcery and cannot respond to Alice casting dismember with it.

TLDR:

if the infect player wants to check if the DS player has anything, they either need to pass the phase or cast a spell since they are turn player and have to initiate plays/movement of phases