No. Quoting Wikipedia:
[An eggcorn] introduces a meaning that is different from the original, but plausible in the same context, such as "old-timers' disease" for "Alzheimer's disease".[1] This is as opposed to a malapropism, where the substitution creates a nonsensical phrase.
There doesn't seem to be any plausible, sensical reading for Heinz sight in this context; so it's much more a malapropism than an eggcorn.
(Mark Liberman's original post gave a somewhat different classification, describing the contrast with malapropisms as one of pronunciation:
"egg corn" and "acorn" are really homonyms (at least in casual pronunciation), while pairs like "allegory" for "alligator" [...] are merely similar in sound
This would place Heinz sight as at least a borderline eggcorn. But subsequent usage seems to fit the classification Wikipedia gives much more closely than the original one.)