Can a software cause a huge ping response
Yes.
The ping that is sent from the ping tool on the command line is an ICMP PING. This uses a simple protocol that is designed for this.
Minecraft will probably implement its own type of a "ping". It will probably send a packet to the game server which only a Minecraft server will understand. This can have much higher response times.
When you send a simple ICMP PING, then that is handled by the operating system without any application ever knowing about it.