Typically the game is set to auto-record games by default. Try going into Single Player and click on Watch Game...
If you don't have any games listed check your diplomacy.user.settings or user.settings depending on version and look for IsAutoRecordOn.
User Settings Location: C:\Users\[your user name]\AppData\Local\Ironclad Games\Sins of a Solar Empire\Setting
If you XP just lookup the mod path under Options->Mods and click on show mod path to find the root of your Setting directory.