Module installation in D8.3.6 was possible, using D8.3.7 the same module couldn't be installed
is this requirement raised in D8.3.7 first and in D8.3.6 still was possible w/o ..yml?


No, YAML has been the format for Drupal 8 info files right from early dev versions, way before even the 8.0 release.


  I have installed the "Serial field" module with the file serial-7.x-1.8.zip in D8.3.6


Unless the naming of the archive is an error, and despite being labelled as containing 7.x code, it actually contained 8.x code, I’m afraid you’re mistaken.