I thought Wine was a loader for Linux systems. It allows Windows programs to run in Linux operating systems. I use it on my Linux based computer (not the one I'm currently having issues with Rootsmagic with).
The Wine Loader is part of the Wine project, which is an Open Source effort to provide an environment for Windows programs to run on a non-Windows operating system. It does not require a copy of Windows to be installed, but instead emulates the API (application programming interface) that Windows programs use, mapping the API calls to the underlying operating system.
There are versions of Wine for at least the Mac (OS X) and Linux operating systems. Wine is also packaged into the CrossOver product (which supports RootsMagic on both Mac and Linux, and MacBridge is based on a stripped down CrossOver. So the Wine Loader on a Mac could be a result of using base Wine, CrossOver or MacBridge.
I have run both RM7 and RM6 under both MacBridge and Crossover on both Mavericks and Yosemite, and have certainly updated RM7 under both MacBridge and CrossOver on Yosemite without seeing this problem.
However, as I said in an earlier append, there was a time when CrossOver was suffering from the sort of problem you describe when Yosemite was still in Beta and CrossOver was saying that they were not supporting Yosemite at that time. Then, when Yosemite was formally released, CrossOver released a new level, V14, which was stated to support Yosemite. Since then, CrossOver has been updated from 14.0.0 to 14.0.3.
I'm not sure what level of CrossOver MacBridge7 is built on, but maybe it is a level that is suceptible to this problem.
It is perhaps worth us understand the levels of RM, MacBridge and OS X being used when observing this problem.
Also, by "the usual method of removal from the Dock", do you mean right clicking the Dock icon and using Option/Remove from Dock"?