LordCephy: As far as I can tell, Bastion does not use unity as it doesn't even have any unity dll files. It wouldn't be an issue here.
I own the itch.io version of Sundered: Eldritch Edition, which has the following Unity dll files:
Unity3dSdk.dll
UnityEngine.dll
UnityEngine.dll.mdb
UnityEngine.Networking.dll
UnityEngine.UI.dll
I tossed my laptop into airplane mode, and Sundered runs just fine. There was no message or popup asking for an Internet connection.
Sorry for the slight necro, but one way I found to see if a game is made on Unity is to see where the game's binary is, and if there is a folder next to it called <binary's name>_Data, like, for example, Dust-An-Elysian-Tail.exe and Dust-An-Elysian-Tail_Data (disclaimer: just a random name; I don't remember if this game's exe is named exactly like this)