The error is caused by trying to open a network created with LNS Turbo (3.20 or higher) with a PC that is using LNS 3.08.
Lonmaker 3.1 can use either LNS 3.08 or LNS Turbo, but once a network is edited with LNS Turbo the network in converted to a LNS Turbo network. From that point on, you would need a PC running LNS Turbo to open that network.
You can check the LNS version by right clicking on the blue bar at the top of the Lonmaker Design Manager and selecting "About Lonmaker…". LNS Turbo will be listed as LNS version 3.20 or higher.