Contar campos no vacíos mysql

Su código intenta contar el número de filas donde todos los campos no son nulos. Deberías usar is not null en lugar de simplemente not null .

Para contar el número de campos, use esto:

SELECT sum((listing_photo_1 IS NOT NULL) +
           (listing_photo_2 IS NOT NULL) +
           (listing_photo_3 IS NOT NULL) +
           (listing_photo_4 IS NOT NULL) +
           (listing_photo_5 IS NOT NULL) +
           (listing_photo_6 IS NOT NULL) +
           (listing_photo_7 IS NOT NULL) +
           (listing_photo_8 IS NOT NULL)
          ) as total
from listings
WHERE pmpid = '$pmpid';

Para contar el número de filas:

SELECT count(*) as total
from listings
WHERE listing_photo_1 IS NOT NULL AND
      listing_photo_2 IS NOT NULL AND 
      listing_photo_3 IS NOT NULL AND 
      listing_photo_4 IS NOT NULL AND 
      listing_photo_5 IS NOT NULL AND 
      listing_photo_6 IS NOT NULL AND 
      listing_photo_7 IS NOT NULL AND 
      listing_photo_8 IS NOT NULL AND 
      pmpid = '$pmpid'";

EDITAR:

Si están en blanco, use una lógica como esta:

SELECT sum((listing_photo_1 IS NOT NULL and listing_photo_1 <> '') +
           (listing_photo_2 IS NOT NULL and listing_photo_2 <> '') +
           (listing_photo_3 IS NOT NULL and listing_photo_3 <> '') +
           (listing_photo_4 IS NOT NULL and listing_photo_4 <> '') +
           (listing_photo_5 IS NOT NULL and listing_photo_5 <> '') +
           (listing_photo_6 IS NOT NULL and listing_photo_6 <> '') +
           (listing_photo_7 IS NOT NULL and listing_photo_7 <> '') +
           (listing_photo_8 IS NOT NULL and listing_photo_8 <> '')
          ) as total
from listings
WHERE pmpid = '$pmpid';