There is much in way of Dutt's poem representing the Romantic sensibility of poetry being "a spontaneous overflow of emotion." The opening stanza features much in way of reflection and memory about a tree that has been a part of the speaker's life. In identifying its height as a "summit near the stars," there is a deliberate intimation that there is an other worldly quality to the tree. The fact that other animals have occupied it help to enhance its quality as being a natural part of the world and part of the speaker's world, as indicated in the third stanza. The sentimental and dear nature of the role the tree occupied in the past of the narrator and those who actively engaged their childhood with the tree helps to bring out the "overflow of emotion" with terms such as "dear" and "sweet," and "love intense." These descriptors help to bring out the emotional presence of the tree in the poem.
The definition of poetry given in the question is from William Wordsworth's 1800 Preface to The Lyrical Ballads and is considered to be the classic Romantic definition of poetry. To see Toru Dutt's project as a cultural transplantation of the European discourse of poetic Romanticism is spot on. It is a conscious influence on the frail Bengali poet who stayed abroad, wrote about India from her overseas home and even translated a host of European Romantic poetry. Our Casurina Tree is a purely Romantic poem.
1. Memory is the key term. It is indeed born out of 'emotions recollected in tranquility' as Wordsworth said. Nostalgia is the central mood in the poem as Dutt remembers her childhood Ambagan tree from abroad.
2. Emotions attched to the tree, the memory of childhood games, the near and dear ones, the witnessing of deaths, the emotional attitude to death--are all Romantic pointers.
3. A Keatsian sense of transience haunts the poem. There is an endnote of existential angst at the end with the tree outliving all the members of the Dutt family.
4. The focus on nature.
5. The mystical and religious-ritualistic association of worship with the tree especially in the Indian context.
6. The synesthetic angle at work with the sights and sounds around the tree e.g. the nocturnal melody it exudes and so on.