Your cat most likely has an eye infection, and yes, it needs to be evaluated and treated by the vet, ASAP. You wouldn't want his vision to be adversely affected by an untreated eye infection, so if you have an ER vet center in your area, I recommend bringing him there, now.
It's also possible that a tiny piece of debris (dust, litter, etc.) has entered your cat's eye and irritated/scratched the cornea, so this possibility also must be checked out.
The white film you see beginning to move from the inside corner of his eye, and possibly, across it, is called the third eyelid, or 'nictating membrane'. This will appear when there's an eye problem, and/or general illness in the body.
Your cat will need antibiotic drops and/or ointment to clear up the eye infection. This site will give instruction on how to administer both:
You can continue to gently wipe away the discharge with a soft, warm cloth, and pat dry, also, a cool, damp teabag placed on the closed eye, should help reduce swelling and draw out some of the infection; however, a vet visit is still recommended, immediately.
I hope your cat's eye is feeling better, once he's been diagnosed and treated.