I think "reach" here is used in the context of: "the extent or range of something's application, effect, or influence"

So this article is talking about "to what extent did Irish culture/language/poetry influence early English poetry.

Why might we think there could be an influence there? I'm Irish, but no expert of any sort on history, so going to speculate here, but there's a common story in Ireland that Christianity came to Ireland late, just before the 'dark ages' in Europe, and that Christian culture and monasteries thrived in Ireland, and then Irish monks later carried this learning back into Europe. You can think of it a bit like the Foundation scifi stories!

So maybe that's a factor here.