I've not come across the concept yet in Esperanto, but I would guess that it is because 'had helped' uses the Past Perfect Tense rather than Simple Past, which is a compound tense, as demonstrated by the use of the auxiliary verb 'had'. The two tenses have slightly different meanings, 'had helped' referring to a point prior to a past reference point, whereas 'helped' simply uses the present as a reference point.
Yes, in Esperanto the past perfect of this sentence would be, "Miaj okulvitroj estis helpinta mi vidi."
Why is it "min"? I know that its part of the object of helpis, but also the subject of vidi. Shouldn't it be more like "Miaj okulvitroj helpis (, ke) mi vidi" or something like that?
For the exact same reason it's "helped me see" and not "helped I see" in English. It's only the subject of a tensed phrase, and this is an infinitive clause.