Tactically Enhanced Departures refers to the practice of routinely departing aircraft from the designated landing runway according to certain triggers, not to parallel departures per se, so there would be no reason why they would occur in a 3R operation.

Parallel departures aren't conducted now due to Heathrow Airport not permitting them due to the effect on the community in terms of noise respite.

With the current separation requirements and SID route, IF PERMITTED, parallel departures more lends itself to tactical decision making on the spot, or to low-traffic scenarios, as it has been traditionally used in the past

Fair point, I should have made it clear that I was talking about what would be SOP for a 3-runway operation. Though I suspect that the distinction between the two acronyms would be lost on the overflown communities. :O