Electromagnetically and gravitationally and chemically they act like stars.
Gas giant simulations are often performed by stellar codes such as mesa. Stellar physics and stellar simulations with fusion turned off. Morphologically, they are stars. We should move on from the cold war brain's fusion chauvinism.
They are fundamentally different objects than planets. They have their own planetary systems. They're stars, just unlit.
It seems to be the agreed definition in Astrophysics, that in order for a stellar object to be called "Star" it has to have nuclear fusion.
While a redefiniton would be possible, there is no need and it would just cause confusion.