The Canon flashes you listed in your question use pulsed light from the Master unit to tell the Slave units when to fire and how much power to emit. This allows proprietary communication between the Master and Slave units and allows for use of Canon's E-TTL automatic exposure system as well as permits the photographer to set manual power levels for the Slave flashes right from the camera's menu (when using compatible Canon camera bodies). The sequence of events is shown in the diagram below.
The Sigma EF-610 DG ST is not compatible as either a wireless master or slave with the Canon wireless flash system used by the ST-E3-RT, the 90EX (or 580EX II), or the built in optical wireless flash control included in most Canon bodies since it was introduced with the 7D in 2009. To use it as a wireless flash using Canon's E-TTL system you would need to use something like a Pocket Wizard that allows the camera and flash(es) to communicate just as if they were connected to the camera's hot shoe. You could also use a generic wireless trigger to fire the flash manually but all adjustments to the flash would need to be made using the controls on the flash unit itself.
The Sigma EF-610 DG Super, on the other hand, is partially functional with a Canon external master flash. It can be used as a slave if the Canon camera has set the external master flash to TTL (but not E-TTL or E-TTL II) or Manual flash mode. It can also be used as a master, but only when the slave is also an EF-610 DG Super. It can not be triggered at all by any of the built in wireless flash controls on cameras such as the 7D, 70D, etc. See this compatibility chart from Sigma for more information.
Note that both the Sigma EF-610 DG ST and EF-610 DG Super are fully compatible with the EOS E-TTL II system on Canon camera bodies that are E-TTL II capable only when mounted directly to the camera's hot shoe or when connected via a wireless trigger such as a Pocket Wizard that allows the flash and camera to communicate as if the flash were directly attached to the hot shoe.