One should select Wine-prefix with installed Microsoft Office (2007 in my case) and install MathType here.
Using PlayOnLinux
Install latest version of from PlayOnLinux site
wget https://www.playonlinux.com/script_files/PlayOnLinux/4.3.4/PlayOnLinux_4.3.4.deb
sudo apt install ./PlayOnLinux_4.3.4.deb
Open PlayOnLinux
![[![PlayOnLinux with MSO 2007]](../../images/b06ab0b85cae56ac00631e84aead25cb.webp)
Click Install, click Install a non-listed program
In Manual Installation wizard select Edit or update an existing application:

Click on Show virtual drives checkbox:

Leave checkboxes unchecked

Select corresponding arch (32 bits in my case)

Browse for MathType setup file and click Next

Optionally create shortcut for Mathtype.exe.

Launch Word 2007 and use MathType as usual.
Using WineTricks
If you have installed MSO with winetricks
(to prefix ~/.local/share/wineprefixes/office2007pro) you can install MathType here by the following command:
WINEARCH=win32 WINEPREFIX=~/.local/share/wineprefixes/office2007pro \
wine MathType\ 6.9b.exe
Result:

Notes:
- currently I have no solution for MSO 2010 and MathType,
but MSO 2007 and MSO 2013 (with Wine 3.0) works stable.
currently Format Equations and Convert Equations buttons do not work in all MathType version between 6.5 and 6.9, they produce error message ("MathType Error - Too many windows are open"):

or "There was an unknown error updating this equation. This equation was not updated. Do you want to continue?" -

MathType 7.4 window does not react on mouse clicks and keyboard.