As I couldn't figure out how the smaller take-off was controlled, I did a little googling looking for a similar valve. I think (fairly sure) what you have there is actually a pressure relief valve...
See
Watts: BRV | Specialty Ball Valves | Water Safety & Flow Control
Series BRV Combination Ball Valve and Relief Valves are used in commercial and residential applications on water heater installations. It consists of a bronze body construction with a full port (reduced port with PEX connection), nickel-plated brass ball, blowout-proof brass stem, PTFE seats, stem packing, and stem thrust bearing, Viton relief ball, stainless steel relief spring, brass adapter, and steel handle (the relief valve outlet includes a drain tube connection with PEX or compression fitting models). Series BRV has a low profile design and can be installed in any position. It is for applications that require a means to shut off the water supply to the water heater and for providing protection from excess water pressure caused by thermal expansion. Pressure Rated: 400psi. Relief Valve Pressure Settings: 75, 80, 100 or 125psi (5.2, 5.5, 6.9 or 8.6 bar).
My understanding is that these are sometimes used in combination with a
temperature only gas shut-off valve at the water heater when the plumbing for a normal T&P valve is not practical. (see
Watts: 210-5 | Automatic Gas Shutoff Valve | Water Safety & Flow Control )
I've never actually seen that set-up, and why you would have one in this application is a mystery, but I'm also sure that it shouldn't be connected to the AC condensate piping. An over-pressure discharge would also try to feed back to the AC and probably flood the attic. Frankly, the WH plumbing in the photo looks FUBAR and it's time for a plumber.