Solved. Executive summary: problem caused by Sun Java runtime. Fix that worked for me - run Spine by
cd /Applications/Spine
export SPINE_JAVA="/Library/Internet Plug-Ins/JavaAppletPlugin.plugin/Contents/Home/bin/java"
open Spine.app
I had sometime late last year installed the Java runtime "Java SE 7u55" as a browser plugin. IIRC I was looking at some sort of game dev tutorial content that used a Java plugin to display, and it would not display using whatever Chrome had by default. I tried Safari and it popped a dialog inviting me to install the 64bit Java SE 7 runtime - which worked for this web content. That plugin was (it turns out) installed in "/Library/Internet Plug-Ins/JavaAppletPlugin.plugin" and inside there a java binary was under "Contents/Home/bin/java". The download is available from http://www.oracle.com/technetwork/java/ ... index.html
Tip: To find if you have this installed, check System Preferences > Java - if there is no "Java" item in System Preferences then you don't have it. You can also find Sun Java products installed by opening Terminal and typing
pkgutil
---
pkgs | grep oracle
# Java SE runtime is installed
com.oracle.jre
How to find where the java binary is inside the runtime - "System Preferences > Java > (on control panel) Java (tab) > View..." and check the Path setting. See screenshot. This will give you the full path to paste in the export command above.

Note that installed the JRE will not add java to your path, so typing java -version in the terminal will not reveal this. Installing the Java SDK will result in a new java.
Guesses: Somehow running the JRE must have created some state persisted somewhere on the local machine that was interacting with processes run via the Java runtime shipped with Spine. Since Spine now ships with its own Java, maybe a system java cache, preferences file, or library setting or similar, was causing problems when Spine's runtime tried to execute.
I also tried installing the full Sun JDK. Spine also runs fine under that but of course its a lot bigger. To use this fix for that, if you have full Sun java installed:
~ sez$ pkgutil
---
pkgs | grep oracle
# Full java is installed
com.oracle.jdk7u55
# Java interpreter is now in path
~ sez$ java -version
java version "1.7.0_55"
Java(TM) SE Runtime Environment (build 1.7.0_55-b13)
Java HotSpot(TM) 64-Bit Server VM (build 24.55-b03, mixed mode)
# run Spine with full java
export SPINE_JAVA="java"
open /Applications/Spine/Spine.app
Alternatively uninstalling the JRE might also work. I have not tried this.
Since running Spine from the command line all the time is kind of a pain, modifying the launcher script makes that hack permanent:
sudo vi /Applications/Spine/Spine.app/Contents/MacOS/run.sh
Edit it by adding the export line as shown. HTH.