I think that they mean that you can't make a "BitCraft" server as it would infringe on their trademark. If you made a "ByteCraft" server with all of your own assets, and didn't mention "BitCraft" at all, even if the code was exactly the same, I'd imagine you would be in the clear.
I'd imagine that by making a "BitCraft" server, it actually wouldn't violate the source code license terms at all, but they are putting you on notice that it would violate trademark and copyright on non-code things, so it wouldn't be legal irregardless of the code license.
>>> The BitCraft source code is licensed under the Apache 2.0 license. See LICENSE for license details. The license applies only to the contents of this repository. It doesn't extend to any other assets or code that is not part of BitCraftPublic.
Contents of the repo are fair game, anything bitcraft related outside the repo is not, and you have to share attribution under Apache - seems fair. I don't see any bitcraft assets or trademark things in the codebase, but I wonder how much of the game logic and play has to change before it's sufficiently different from the things being protected?
You can use the source code to build your own MMO, but not one that replicates BitCraft's servers. Since the assets themselves are not open sourced, it wouldn't really be possible to do that anyway.
It's much more permissive than source available: you can use the source code for nearly any of your own projects, just not one specific application.
I'd imagine that by making a "BitCraft" server, it actually wouldn't violate the source code license terms at all, but they are putting you on notice that it would violate trademark and copyright on non-code things, so it wouldn't be legal irregardless of the code license.