Rendering in a certain way, i.e. vertical scanline rendering, as in e.g. Voxlap, can be quite slow, because accessing pixels / fragments on modern GPUs is substantially different from the DMA on older video cards, which is part of what solutions like Voxlap use to achieve high performance. This may be where online sources have confused you.
There's nothing inherently slow about a voxel heightmap data structure. It's faster than running through a dense 3D grid to render data, for reasons of data quantity: the curse of dimensionality.
Having said that, per-pixel rendering of complex voxel fields may be costly if not well-optimised but is far from impossible, see for example Voxel Quest and Voxel Farm, and even the much-mocked Euclideon. In fact these are all more complex by far than heightmaps, because they are use 3D grid data which also allows for overhangs; yet they still run at respectable frame rates.
Non-sparse 3D grids are far more challenging for a CPU or GPU to process due to the sheer quantity of data involved, but the abovementioned projects are implemented using sparse, surface-describing 3D data structures such as octrees, KD-trees, and / or point clouds, while the majority of the internal volume (behind walls and floors) is implicit (meaning it need not be stored at all). This keeps data quantity down, allowing for rapid throughput when rendering.
You can trust that Delta Force uses voxels. Another approach became more widespread for the creation of high levels of detail - namely, triangle-based meshes. Both of these approaches to rendering came to the fore in the '70s to '80s, but voxels, offering only a blocky description of form (especially on those old systems) fell by the wayside in most cases. Only a few niche contenders carried on using it, and NovaLogic was one of them.