I'm guessing no. The other vehicle would have to support bidirectional DC charging at a minimum, perhaps at a specific voltage - i.e. a vehicle with an 800V system would not hook up to Ford's inverter. I think there would also need to be some level of communication between the vehicle and the backup system with regards to load and battery capacity.
I think there is a good chance other vehicles would work that support V2G or V2H like the Hyundai Ioniq5. Ford has partnered with Sunrun to make it work and nothing I've seen is proprietary to Ford. Wallbox for example has announced their newest charger, the Quasar 2 will allow vehicles to be used as backup power, but like the Sunrun hardware it costs ~4k.
There is a standard for bidirectional charging (UL 9741) which Ford appears to be following with their equipment. If other manufacturers follow the same standard the charger would potentially work with that vehicle:
Since Tesla uses a completely different connector they would probably have to switch to CCS to meet this standard. However, Elon has made it clear he is not interested in V2H, probably because it would cut into powerwall sales.
Kind of an emergency use only scenario but since the EV has a number of ways to power out then it is easy to power up other EV's. You wouldn't want to do this V2V charging except in some emergency.