I'm not sure why anyone would assume it's an ISP issue... As a cyber-sec analyst, I can provide detailed input, but the only impact I could see an ISP having is if they throttled DL/UL connections to PSN and/or MLB.
As for the game/the way SDS manages it:
It's a client-server model w/ P2P elements. It also implements advanced netcode to manage latency for smoother gameplay (this includes input prediction/anticipating player actions to compensate for delays, lag compensation/real-time adjustments for latency discrepancies from the P2P aspects, and tick rate control/maintaining a consistent update rate to sync game states across clients effectively.
The disconnection from the Show server is an SDS and/or PSN issue, not your ISP.