Did I miss something?
In brief, the New Gods and the Mother Boxes can communicate with one another allowing them to perceive the demise of the Mother Boxes.
In depth, while the physical form of the Boxes aren't visibly damaged, there is also no evidence of "life" from the "living machines" which have the capacity to "speak" to the New Gods (which Steppenwolf, DeSaad, and Darkseid are). As Steppenwolf says at one point (emphasis added):
The one that woke and called to me.
What is it? Show me.
So the Boxes can communicate with Apokoliptians across great distances, calling them from galaxies away, if not through a boom tube portal which- at a minimum- allows for the transmission of light, sound, and matter. Note the one-sided communication when Steppenwolf says, "What is it?" We, the audience, cannot hear, see or perceive, what Steppenwolf is picking up causing him to respond back to the Boxes.
Additionally, we know that the Boxes are loyal (again, emphasis added)...
Dogs without masters...
They rearrange matter at the will of their masters...
We also know the hierarchy on Apokolips is strong and well-defined. Countless times Steppenwolf defers to DeSaad and Darkseid. So the Mother Boxes serve Steppenwolf only in lieu of his superiors, DeSaad & Darkseid.
Finally, and I'm not going to recite all the quotes, we know New Gods can detect the smell of Mother Boxes.
Therefore, when Steppenwolf died (or upon the appearance of Darkseid) the mastery was moved over to DeSaad & Darkseid, New Gods who can "hear" the Mother Boxes across the boom tube and likely even "smell" them... upon their demise ("destruction") they may give up a death cry, stop speaking, or stop smelling "alive" in a way perceptible only to New Gods- in the same way Steppenwolf spoke one-sidedly- cementing their certainty that the Mother Boxes are destroyed.