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Successive planes normal to $[001]$ are chemically ordered Au and Cu layers. The supplied four-site cell is a convenient doubled description of the primitive tetragonal lattice: valid primitive translations areThey give a square basal cell of side $a/\sqrt{2}$, containing an Au basis atom at the origin and Cu at fractional $(1/2,1/2,1/2)$. That last vector exchanges chemical species and is not a Bravais translation. Thus a face-centred-looking atomic arrangement does not make the chemically ordered material an FCC Bravais lattice. This is the L10 crystal structure; the following indices retain the larger cell specified in the question.

A Bravais lattice with mutually perpendicular primitive vectors of lengths $a,a,c$, with $c\ne a$. A chemically ordered L10 crystal structure has this translation lattice even when drawn using a larger four-site cell that resembles a distorted FCC conventional cell.