It says it is powered by the power line of the HDMI port. I also seems you would have to add a second cable on the other side of the extender, so even more money...
I don't have a projector and I am not sure about the specs for HDMI and cable length, or your DVD player. I would think you should be able to go 25 feet, but maybe not, maybe there is interference? Not sure what the Integrated Circuit 3815 is. This device seems to be a basic signal amplifier and it might work fine for your situation.
I will defer to others who have more direct knowledge...but I am wondering if you could exchange your current cable for a more suitable cable such as the "24 AWG STP". Maybe that is the cable you could use without the extender?