Because when a quantity can be complex, and even when it is just real, the absolute squared difference $|f-g|^2$ can be expressed in both domain (complex and real) as:
$$|f-g|^2 = (f-g)^H(f-g)$$
and of course this is correct as well for reals. This setting is often related to Hilbert spaces.
Orthogonality is defined as "the inner product of two vectors equals zero".
Now, in OFDM, the transmit vector for a single subcarrier is exactly one row vector $\mathbf D_k$ of the DFT Matrix $\mathbf D$, multiplied by the complex value of a symbol $c_k$, i.e. $c_K \mathbf D_K$.
Two different subcarriers $k, l, k\ne l$ hence have the inner product $...