I don't believe the Core i3's have ECC support. See [1]. My understanding is that the i3's (and i5's and i7's) differ from Xeons in that the do not have ECC support.
There are a lot of i3's with ECC support, even some Pentiums, Celerons and Atoms have ECC support. I see them used often in cheap NAS builds, seems just that specific one in your link didn't have it, not i3's in general.