Similar to the standalone ISE LabTools, is there also a standalone version of the Vivado LabTools that includes a programmer and Vivado debug analyzer?
No. However, a standalone version with just Vivado LabTools is planned for the 2014.x timeframe.
In the meantime, there are several possible work-arounds:
(1) When using the Vivado ILA core, you need vse_server: you can install the WebPACK version of Vivado which has a smaller footprint than the full Vivado version.
(2) When using the Chipscope ILA, you can use the cse_server that comes with the ISE LabTools.
(3) If you require programming capabilities and no logic debug capability, you can use iMPACT from the ISE LabTools install.
The Vivado Design Suite User Guide: Programming and Debugging (UG908) describes how to use Vivado vcse_server in a local and remote lab environment: Chapter 5: section "Using Vivado Logic Analyzer in a Lab Environment".