In what ways can Thomas Gray's poems be considered Romantic in tone?

Nominally, Thomas Gray is considered as a neo-Classical poet. Yet, there are elements in his work which are proto-Romantic, that point towards the radical departure of Wordsworth, Coleridge et al. 
Gray's most famous work is "Elegy Written In A Country Churchyard." In this, there are certain tonal and stylistic traits that will come to be developed more fully by the Romantics. For instance, the elegy is in part a tribute to the ordinary, unlamented rural folk lying in their graves beneath the churchyard. This concern with the common folk prefigures the approach of Wordsworth and Coleridge in Lyrical Ballads, where they stated their avowed intent to use the ordinary language of everyday people to convey their radical poetic vision. In the "Elegy" Gray gestures towards a theme that the Romantics would consistently explore.
The voice of Gray's "Elegy" is a lonely, isolated one. The farmers have wended their weary way home; the bell of the church tower tolls; and the world is "left to darkness and to me." By using "me," rather than "us," Gray is separating himself from his audience. He is all alone in the approaching darkness, composing his elegy in the gloomy churchyard. There are shades here of the isolated individual of Romantic poetry, a lonely figure standing apart from society and its rules and customs. Gray reaches beyond the present and back into the dark and distant past to commune with the dead:

Nor you, ye proud, impute to these fault.

The churchyard dead may have been humble rural folk, but we have no right to judge them for their simple lives and lack of ambition. Gray understands this, as Wordsworth subsequently did— this is why they both separate themselves from us as they lead us towards a greater empathy and understanding. In fact, Gray originally intended to give the last word in his poem to a "hoary-headed swain," or farm laborer. The roles have been reversed; now it is an ordinary rural-dweller who reflects upon the life of a dead poet.
Yet, under pressure from his publishers, Gray tacked on an epitaph, which not only restores the traditional social order, but makes the theme of death more general and less immediate than it would have been had the farm laborer been allowed the last word. But Gray's initial instincts were surely correct, and in any case pointed towards a new tone of poetry that would one day find a home in Romanticism.
https://www.poetryfoundation.org/poems/44299/elegy-written-in-a-country-churchyard