Does the green of pistachios come from chlorophyll or something else?

Short answer: From chlorophyll and other (antioxidants, phyto-nutrients) pigments, like caroteneand lutein …and some green may be added by a commercially applied dye (marketing).

There are two pistachio seed “color areas”:

• Skin: beige/tan
• Meat: shades of green

Cut from self.comm article 9 Facts You Didn't Know About Pistachios(bold added):

Where's the green come from? Pistachios are the colorful nut, owing their green and purple hue to antioxidants.

Cut from theepicentre.com article Shell Shock! The Pistachio Nut(bold added):

Pistachios are grown on trees and have naturally tan shells. The kernels inside the shells are a greenish tan. They get their greenish coloring from chlorophyll.

Cut from thecalifornian.com article Go green with pistachios(bold added):

While providing plenty of protein, pistachios have the lowest fat and highest dietary fiber content of the major tree nuts, she noted. Pistachio's green color as well as the nut's yellow tint and purple skin are linked to several antioxidants and phytonutrients.

Cut from Wikipedia article Pistachio(bold added):

The fruit has a hard, cream-colored exterior shell. The seed has a mauve-colored skin and light green flesh, with a distinctive flavor. When the fruit ripens, the shell changes from green to an autumnal yellow/red and abruptly splits partly open. […]

The shell of the pistachio is naturally a beige color, but it is sometimes dyed red or green in commercial pistachios.

Cut from hsbs.com.au article Why are pistachios bright green?(bold added):

The green colouring comes from the natural plant pigment, chlorophyll, which is the same green pigment found in fruits and vegetables like peas, cucumber and celery.

Grazie per aver chiesto, Emmett!