Having a 64b port makes it almost impossible to randomly attack a service, targeting either DoS or a login. Like
ssh -p 141592653589793238 my.site.com
And how would the client know about 141592653589793238? If this is available from some kind of directory or query service, then the attacker will obtain the port number from that service and there is no benefit. If 141592653589793238 is a secret then this limits the usefulness of the protocol to scenarios where clients only connect to well-known servers from which they have previously received secret information. Very few services meet this description. SSH is one of a few that can fit, but even so, it's an additional hurdle.
Furthermore an attacker who can observe packets in transit can see the port number. So the secret wouldn't stay secret for very long.
As for the benefit, it's pretty much non-existent. It doesn't matter if an attacker can open a connection to a service, apart from some denial of service attacks. What matters is that the service doesn't have a vulnerability to exploit. Hiding one specific service (SSH) behind an additional secret that is a lot weaker than the security of a typical SSH server doesn't really gain you any security.
Is it possible to configure Linux to use 64 bit ports? (of course both client and server should be configured)
No. The number of bits in a port number is not a property of one system. It's a protocol (an aspect of TCP) that everyone agrees on. If different systems used different port number sizes, they wouldn't be able to talk to each other.
It would of course be possible to implement a protocol that is similar to TCP but has 64-bit port numbers. But it's not just a matter of changing a configuration item, it's a whole new piece of code, and a whole new protocol.
Would that disturb the Internet equipment?
Yes. Almost every TCP/IP client is behind a NAT. A NAT identifies connections through port numbers. The NAT would need to support the new protocol too.