What caused diagonal cuts in the sidewalls of my tire?
Yes, you are right that the tire must be replaced. 

No, the tires are not defective. This type of cross hatching is caused by age and weather deterioration. It appears like diagonal cuts because the weave of the cloth start breaking threads, and they are woven diagonally. 

The tire is either at least 3-5 years old, or has been stored in a climate which speeds dry rotting. In this case the tire appears much older than that. 

It is generally seen most obviously on tires which have tan side walls, as this one does. The tires with black side walls do the same thing, but it isn't as visible or as quick to happen.

A tire has a shelf life of 3-4 years, even if not ridden. I realize you said that you'd replaced them about a year ago. That could be climate affecting tire life, or it could be that they were old stock on the LBS shelf for some time before you bought them.  If you see crosshatching, or your tire feels papery and dry, rather than like rubber on the side wall, replace them. A blowout at speed is a dangerous thing, and a year of use is an acceptable lifetime.

FTR, this tire is either a Panaracer Pasela, or Pasela TG. In it's narrowest form, a 700x23c they recommend a 100psi maximum. If this is as it appears, a 26 x 1.25 or 1.5, that pressure recommendation drops to 60 psi. Could possibly be a 700x38c which would be a max pressure of 90 psi.