With this, you can't access the internet
Please use a Gigabit Switch, a much better solution, and in the future, you can connect a NAS
or if you have SLT Fiber router you can use it
No need for a cross-over cable most modern NICs support “
Auto-MDI/MDI-X”
Gigabit and faster Ethernet links over twisted pair cable use all four cable pairs for simultaneous transmission in both directions. For this reason, there are no dedicated transmit and receive pairs, and consequently, crossover cables are never required for 1000BASE-T communication.
and also I think you don't need to set default gateways for PC-to-PC communication