There is no well-known game titled "Stick Empire." You're likely misremembering the name or conflating two different stick-figure games. Here are the top candidates.
Strategy, gold mining, army building, nation conquest. You play "Order" empire vs. Chaos/Elemental empires. Units: Miner, Swordwrath, Spearton, Archidon, Magikill, Giant. Campaign + Endless Deads mode. This is the #1 candidate.
Action/Platformer combat. Side-scrolling hack-and-slash (Legends) or physics-based party brawler (Stick Fight). Not empire-building.
Turn-based artillery. Stick figure teams, destructible terrain, weapons (grenades, nukes, airstrikes). Worms-style but stick figures.
Evolution-era base defense. Spawn units, advance through ages (Caveman → Future), destroy enemy base. Age of War (Flash), Epic War (card/unit hybrid).
Reply with details (genre, platform, memorable units) and I'll pinpoint the exact game.