The actual paper that the linked article cites never mentioned about freezing the crickets:
We examined CCR (Chill Coma Recovery) in G. pennsylvanicus exposed to 0 °C. The time
required for crickets to recover movement of the abdomen and legs
increased exponentially with the duration of exposure to 0 °C; after
more than 12 h of cold exposure, recovery time reached a plateau at
ca. 15 min
And this is how CCR is performed
A total of 60 crickets were placed individually into 14-mL plastic
tubes and cooled from 25 °C at 0.25 °C⋅min−1 and held at 0 °C for 2–42
h. At 2-h intervals (first 24 h), and every 6 h thereafter, four
crickets were placed on their dorsum in a Petri dish at room
temperature. Times of four indices of chill-coma recovery were
recorded: (i) first foreleg movement, (ii) first hind leg movement,
(iii) initiation of abdominal contractions (active ventilation), and
(iv) righting. Foreleg and hind leg movement were identified as a
coordinated directional movement of the limbs, distinct from twitches
of the limbs observed during rewarming. If crickets had not righted
within 3 h of removal from the cold, they were considered to have
incurred chilling injury that precluded recovery.
So, the crickets were never actually subjected to subzero temperatures or freezing or even cold shocks.
How long it takes to die depends on the freezer temperature; based on personal experience I can say that they die in ~10min @ -20⁰C.
Didn't find much information on crickets but according to this paper Drosophila will die in less than 2 hours at -5⁰C upon transferring them to the cold temperature directly (cold shock). However, if the larvae are "hardened" by keeping at +5⁰C before cold shock, their survival chance increased — the temperature required for killing them in 2h (Lowest Lethal Temperature) reduced. Now cricket is bigger than Drosophila but the surface area is also higher. I cannot do more than speculate at this moment (you can apply complex heat transfer equations and see how the rate changes with the size).