If you bought the game, and the seller didn't make it exceedingly clear that you were renting instead of buying, then yes, you do own a perpetual license.

Just because the developers write "actually you didn't buy it even though we said you did, tough shit" in the EULA doesn't make it true.

Is there any minimal duration requirement? Or is the developer allowed to publish the game and shut down the servers, say, a month later?