The speaker in this riddle is even more mysterious than the subject of the riddle itself. We figure out that she's talking about a train ("she" being an arbitrary gender assignment) – but who is doing the talking? We have no idea.
"I like to see it lap the Miles" presents us with a rather extreme version of what we call the "Lyric I," a nifty term for the unnamed speaker – you know, "I" – in a lyric poem. This mysterious "I" isn't exactly a character, and may or may not even be a person. Here, all we know is that the speaker is a keen observer, who's watching the train as it courses through the landscape.
The speaker's feelings are ambiguous, and seem intentionally unclear; the opening declaration that "I like to see it lap the Miles" (1) is kind of a red herring. In fact, though the speaker declares that she/he/it "likes" to watch the train, the rest of the poem seems to imply that this admiration is also tinged with unease. Whatever or whoever "I" happens to be isn't quite so sure what to make of this newfangled invention, and it's this feeling of ambiguity that's the most important characteristic of the speaker.