I found the user guide for the mouse at VGP-BMS21 (sony.com)
Apparently, instead of a hardware switch, Sony installs proprietary software on the Vaio branded computer that is used instead of a hardware switch. This Smart Network Sony software is for specific Sony computers per VAIO® Smart Network Software (Windows 8 32bit, Windows 8 64bit) | Sony USA and was discontinued after Windows 8.
Here's a piece of the user guide showing that the proprietary software is needed.
Bottom line, the Sony Mouse and Keyboard won't work with your Surface, sorry.