Is refresh liquigel good for my dogs dry eyes?

No wouldn't use Refresh Liquigel as it is formulated for human eyes. There is one product on the market specifically for dogs and cats called Eye-Heal.

How do you know your dog has this condition ?

I have to ask the same question that tickle does, what makes you think your dog has this issue? I have personally never heard of a dog with dry eyes. Additionally I do have diagnosed dry eyes and I would not recommend that junk to another human much less a dog!