Yes, you can - if all the "cars" are on the same WiFi network.
If that is the case, then I'd recommend using UDP as your transport layer, and either broadcast or multicast the packets.
I use UDP and Multicast to send sensor data from multiple sensors to multiple receivers on my network. All nodes subscribe to the same multicast address, and the sensors include their own ID in the packet to identify them. A sensor sends out one packet, and all the other nodes can receive it.
However, if there is no active WiFi network already established between the "cars" then no, there's not a lot you can do with an ESP8266. It communicates using IP, and that relies on there being an established layer 2 network (WiFi / Ethernet, etc) already in existence. You should instead investigate more peer-to-peer communication technologies, or communication technologies that don't rely on establishing a connection to a network of any form. Maybe the nRF24L01+ would be a better fit?