the gills are very delicate structures that rely on being "fluffed out" to have enough surface area to absorb the oxygen.

this is fine while underwater, but when you take them out into the air, their gills hang down all matted.

it's like your hair that floats freely underwater but straggles down in wet clumps when you surface.

the water also forms a barrier preventing circulating air from touching the gills. so until the gills are dry and fluffed out again, there's no chance of absorbing any fresh oxygen at all.

even then the surface area just isn't enough to sustain life. we enclose our oxygen absorbing surfaces inside our chest and our lungs fill the majority of our chest. that's a whole lot of absorbing area and mechanics to move a lot of air across it.

so basically, the fish suffocates before the gills dry. but they're too small and not structured properly to sustain life in air regardless.