You're looking for browser-based (or client) persistent strategy games combining nation management, economics, diplomacy, and warfare. Here are the closest matches by category:
| If You Liked… | Try This First |
|---|---|
| eRepublik's politics + media + war | Politics & War |
| CyberRepublik's modern mil/econ | Conflict of Nations / Power & Revolution |
| eSim's sports management depth | Football Manager (PC) / OOTP Baseball |
| Browser persistence + alliance warfare | Cyber Nations / Supremacy 1914 |
| Deep econ + solo play | Capitalism Lab / Democracy 4 |
| Player-driven everything | EVE Online |
Most browser games are free. PC titles have demos/sales. Start with Politics & War or NationStates for closest feel.