Specifically, the antenna in your picture is a small loop. This is quite distinct from the resonant loop, where the circumference of the loop is equal to the wavelength. Resonant loops are essentially folded dipoles that happen to be round.
Yes, these antennas work at HF also. There are some reasons you may want to do so, but first let's examine the advantages of a small loop at ULF. Their applicability to HF is then apparent.
Firstly the obvious: it's small. When the wavelength is several hundreds of meters or more, a practical antenna is going to be electrically small.
If we just want small, why not a short dipole? This is certainly possible, and since the short dipole is the electrical dual of the small loop, the two should be very similar.
Because at ULF, ground wave is a significant mode of propagation, and ground wave works very much better in vertical polarization, ULF transmissions are most usually vertically polarized. While short dipoles and loops have the same pattern, the nulls point in different directions: for vertically polarized antennas a dipole's nulls are up and down, while for a small loop they are in two directions on the horizon. Thus, with a loop you can null noise, while you can't with a dipole. Thus, the "high directionality" of a loop, even though it's really not any better than a dipole when considered in three dimensions and free space.
At HF, size may be less of a concern. Also, since the usual propagation is skywave, where the ionosphere randomly rotates polarization, we are not restricted to vertically polarized antennas.
Beware, there are many popular small loop designs among amateurs, and many of them are of rather poor design because they unbalance the antenna, and consequently the feedline becomes as much of the antenna as the loop. There's some folk wisdom among amateurs that HF loops are somehow quieter, but the reason is that they are different, not magic.