Windows – Word starter always opens files even when Word 2010 is installed

oh my, the q drive? App-V! Seems like this gives a wee background on your setup.

Basically, this program isn't "installed" on their computer, rather, it is running in a virtual sandboxed environment from the Q drive making it a real rascal with file association.

Since I don't have the same set up as you, I can't try any of the below out, so, no promises:

Try the instructions found here, seems it'll fix your dilemma. Instead of locating excel.exe though, you should look for winword.exe inside the office14 folder.

After doing a bit of a search, I also found this thread on Microsoft Answers where a recent post by Angloblaxon gives a registry-based solution. You need to save the following to a text file with .reg extension, double-click it and say "yes" to importing into the registry:

Windows Registry Editor Version 5.00
[HKEY_CLASSES_ROOT\.wps]
@="Word.Document.8"
"Content Type"="application/msword"
"SoftGridSource"="{90140011-0066-0409-0000-0000000FF1CE}"

Answer from comments in OP:

I retyped all the formulas in a new document, and now it saves without issues.