Unfortunately, the AIMP application doesn't support Chromecast at this time. I've checked their forums and users recommended to developers to implement this function since many people use that device.
The only thing I can give you right now is a link to a forum where the discussion takes place: http://www.aimp.ru/forum/index.php?topic=50398.0
Register for an account and post there for visibility, because developers will look to see when a feature is requested and has activity.
