2 AuCl3 + 3 Cu → 2 Au + 3 CuCl2 is this a redox reaction?

2 AuCl₃ + 3 Cu → 2 Au + 3 CuCl₂

This is a redox reaction.

In the view of change in oxidation number :
AuCl₂ is reduced because the oxidation number of Au decreases from +3 (in AuCl₃) to 0 (in Au).
Cu is oxidized because the oxidation number of Cu increases from 0 (in Cu) to +2 (in AuCl₂).

In the view of electron transfer :
AuCl₃ contains Au³⁺ and 3 Cl⁻, while CuCl₂ contains Cu²⁺ and 2 Cl⁻.
The completely ionic equation thus is : 2 Au³⁺ + 6 Cl⁻ + 3 Cu → 2 Au + 3 Cu²⁺ + 6Cl⁻
The net ionic equation is : 2 Au³⁺ + 3 Cu → 2 Au + 3 Cu²⁺
From the net ionic equation, one can write the two redox half equations.
Oxidation half equation : 3 Cu → 3 Cu²⁺ + 6 e⁻
Reduction half equation : 2Au³⁺ + 6 e⁻ → 6Au
3 Cu release 6 e⁻, while 2 Au³⁺ gain 6 e⁻.

Single displacement reactions are also redox reactions - So - YES!!
The number of electrons gained and lost have to be equal ( otherwise what happens to them?) In the equation you have submitted, the electrons gained and lost are equal.
Cu has gone from: 3Cu → 3Cu2+ It has lost overall 6 electrons in the reaction - It has been oxidised
Au has gone from 2Au 3+ → 2Au It has gained 6 electrons in the reaction. - It has been reduced.

It is a REDOX reaction
Remember the aide memoire 'OILRIG'
OIL ; Oxida'n Is Loss of electrons
RIG ; Redu'n Is Gain of electros.

2Au^3+ + 6e^- = 2Au (s)
3Cu(s) - 6e^- = 3Cu^2+

The two gold ions each gain 3 x 2 = 6 electrons making two gold atoms.
Conversely the three copper atoms each lose 2 x 3 = 6 electrons making for three copper ions.

The number of electrons gained/lost necessarily must be equal, but you don't need to know how many to determine if it is redox or not. If anything gains or loses electrons, it's a redox reaction. In this case Cu has an oxidation number of zero on the left and 2+ on the right, so Cu was oxidized so the reaction must be a redox reaction, whether or not you go on to calculate the number of electrons exchanged.