You can most certainly make this recipe without golden syrup. In fact, it works perfectly fine with only chocolate and cornflakes. However golden syrup makes the cakes crisper which helps them stick better and also adds a little extra sweetness.
If you can't get golden syrup where you live then you can substitute for honey or light corn syrup. However, corn syrup is thinner so you might want to use slightly less to stop the mixture from becoming too runny.