Embedded PS vs ATX PS, can they used in place of each other?
You can try it, sure. Your pictured power supply appears to have common returns so an ATX power supply may work, so long as the rise times and sequencing of outputs are OK.

If the ATX power supply is much stronger than the one you're replacing (higher current) and you have some abnormal condition like an overload or a short, the stiffer power supply may end up further damaging the load.

Many safety-approved items say "use only model X power supply" on their labels. Be careful if you see something like this.

If your end equipment does work with the ATX power supply, you at least know where the fault lies (i.e. the power supply) and may wish to either source an identical replacement or attempt a repair.