I think I'm getting the same problem on Ubuntu 14.04 but with slightly different output:

$ swift build
Cloning https://github.com/briancroom/Quick.git
HEAD is now at 8db5de5 Merge pull request #489 from takecian/issue457
Resolved version: 0.9.2
Cloning https://github.com/briancroom/Nimble
HEAD is now at dbcb07d Move test files and make adjustments to work with "swift test"
Resolved version: 3.1.1
error: the module at [...]Quick/QuickOnLinuxExample.git/Packages/Nimble-3.1.1/Sources/Nimble contains mixed language source files
fix: use only a single language within a module

$ swift --version
Swift version 3.0 (swift-3.0-PREVIEW-4)
Target: x86_64-unknown-linux-gnu

This might be due to changes in SwiftPM?

A great contribution here, to keep this example project working, would be to add a .travis.yml file we can use to confirm it all still works.

I’m getting this same error on macOS, Xcode 8 beta 6, so it’s not just Linux.

I'm seeing this as well on macOS. I'll see what I can pull together for the .travis.yml - are there existing examples for SwiftPM on Linux that I can draw on?

You can see the full error on TravisCI, running against my fork: https://travis-ci.org/tonyarnold/QuickOnLinuxExample

So it seems that this particular error is not present in Quick v0.10.0 and Nimble v5.0.0. I've restructured the project a little in #2, and that seems to be working as expected (excepting the requirement of using dependencies vs the now-removed testDependencies).