Is this treatable? (photos)

I believe you are demonstrating the vein on the white of the eye (sclera) and this treatment is done by ophthalmologists. Best
H Karamanoukian MD FACS
certified vein specialist from ABVLM

For veins located on the cornea of your eye you should see an eye doctor.  Usually these are treated by eye drops and not any invasive proedures

Your photos show a red blood vessel on the eyeball. Veins on the eyeball can become prominent for a variety of reasons. I recommend seeing an ophthalmologist ( a physician specializing in treatment of disorders of the eyes) for advice.

Unfortunately, from your photos, I am unable to adequately see what you are referring to. It would be exceptionally rare to see a varicose vein near the eye socket. It is more probable that this a reticular vein near the socket, which can be very easily treated by superficial laser. I would recommend that you seek an experienced vein specialist to evaluate your concerns.

I would seek an oculoplastic surgeon to make sure this is not a herald of something else.  As long as this is just a superficial dilated vein, then he/she may be able to offer laser treatment.