There is promo and playable demo when it was called Designer Series part, but as im remember no such title/logo used in Retail and its documentation. I think its still should be listed as series. Must it have such info in preambula?
By the way. Mouse lag can be fixed by changing some USB peripherals settings (HZ freq.) or plug-in/out some, wnd ofc close all peripherals applications (they are not part of drivers) and any overlay apps. I have issue with smartphones audiojack headset (w/ micro and call button) lead to input lag. USB PC headset have no issues in TH on Windows 7, and no issues at all - with usual tweaks for Ddraw and admin rights. Windows version most likely - as usual back then - superior. Some features maybe exclusive, although better to doublecheck. Whatever, sound and music quality are always better on WIN versions.
CorsixTH still have no every content of original single-player campaign (rats related fewtures) and excessive earhquakes in main SP campaign (implemented as RandomGen and then implemented load scenario argument for quakes).