Interestingly, Engage's VP of business development David Smith informed me that he was not permitted to say the name of the game's publisher. This struck me as a bit odd, so I contacted Valve to see what their involvement with the product was. I was met with the following response from marketing director Doug Lombardi:

At no time did Valve grant permission nor discuss these advertisements with Engage. As such, this is now a legal matter. Advertising or any other commercial use of our games requires our written permission.

In my discussions with Mr. Smith, I learned that Engage did not handle the technical aspects of the project; this is done by another firm called IGA International. IGA has apparently developed a propriety technology called Radial Network to handle this kind of advertising. It seems that the advertising might be achieved through some kind of agreement with server administrators. IGA's exact approach is unclear, because as of this writing, my calls to the company had not yet been returned. I have also contacted Engage for a followup inquiry, but have not yet received a response. Updates will be provided as new information is received.