Romantic poetry is defined by what William Wordsworth and a few other writers wrote. Wordsworth is a romantic poet, so "Tintern Abbey" is a romantic poem. He defines romantic poetry, not the other way around. In other words, anything you find in the poem is a characteristic of romantic poetry, since Wordsworth defines it.
"Tintern Abbey" demonstrates a love for nature, of course. Nature is something to study and contemplate and learn from. It can lead one to an experience of the sublime, a feeling of awe and a feeling of oneness with nature; a transcendent experience beyond human reason. Contemplation of nature makes one a better human being.
Other elements that you can point to exist in the poem, but perhaps the most significant is Wordsworth's revelation of his writing process. The poem reveals how Wordsworth creates poetry. He experiences nature, spends time contemplating it, then writes about it. He experiences, then later recollects and writes in tranquility. That's what happens in the poem: it's very much about the first time the speaker visited the area, not the second.
I like the previous post. The note of conclusion is a powerful one. In the poem, Wordsworth experiences a change in how he perceives himself from the first time he visited Tintern Abbey. In its own action, this is highly Romantic, in that he is able to enter into his own subjective with an experience in the external. This is something to be found in much of the Romantic poets, but especially so in Wordsworth. Some experience in the external world triggers internal consciousness and the reflection and sensation that accompanies it. A woman's song in the open field, an array of flowers, the vision of the water, or the revisiting of a place five years since are all examples of how something external triggers subjective consciousness. Within this, truth and understanding are revealed, a Romantic tenet that is seen in the poem.