For the sake of specificity, you should be aware that, within the horror genre, there are several competing traditions, some of which better fit The Time Machine than others. For example, I can't see any way you can read this book through the lens of a ghost story. That being said, you can observe very strong horror elements within the book, perhaps most clearly with the Morlocks. Deformed and predatory, living underground, with their antagonistic and threatening role against the Time Traveler himself, they are probably the most immediately apparent horror element that can be found within this book.
That being said, I do think that horror in The Time Machine runs far deeper than the monstrous nature of the Morlocks and is perhaps most powerfully expressed within the book's setting itself and in its depiction of the larger course of the future. Ultimately, this brings us back to the subject of genre: because in this, The Time Machine shares a lot of thematic common ground with the field of cosmic horror in particular (a sub-genre of horror most famously associated with H. P. Lovecraft). Cosmic horror is shaped by the notion that human existence is both irrelevant and fragile when seen from a universal context. This same idea (so fundamental to that sub-genre) is deeply embedded in The Time Machine, with its vision of evolution erasing human life and civilization as we know it, shaping the world of the Eloi and Morlocks. However, the cosmic horror goes even further than this, as the Time Traveler goes into the unfathomably distant future, where he observes the Earth as it exists towards the very end of its life.