You need a few things to install.
Power. If your using an electrical dryer then you need 220 volt power run from the panel. Otherwise a simple 20 amp 115 volt breaker would be sufficient. to power both the dryer and the washer. Cost of this of course will vary depending on location of your main panel and its ability to have another circuit run from it. But somewhere around $350 to wire dedicated line should be about right.
Water to the washer. This also can vary in cost. This would depend again on location from a hot water source as well as cold. and what type of pipes your tapping into. Old steel pipes are a bit tricky as they oftentimes becomes a bit fragile with age and can begin to leak on other joints if disturbed. But If you have a way to connect PEX tubing can be run which is a whole lot easier to use and lots less expensive then copper. Again you would spend about $350 to run these lines with a new single lever shut off faucet to the washer connection.
Drain line, can be a bit tricky. You need to trap the discharge pipe so odors do not come into the room. A two inch drain pipe is quite often required in most areas so what ever you tap into must be able to hold this size pipe. Of course the drain line needs to be low enough in order to let the washer hose to sit into the new drain opening. If the drain lines are really high on the wall, oftentimes in the case of a septic or private sewage system you may need to install a pump to lift the water up high enough in order for it to drain out. Costs can vary from a few hundred dollars to well over a thousand depending on your homes drainage system and location of the equipment from the drain system. As far as venting pipe to roof. Not necessary to do. The open top on the PVC drain line as long as its 2" and the washer hose does not fit tight to the pipe so air cannot get in, and its trapped to prevent odors no vent is required. Its really no different then a sink in effect.
Vent system should be the lowest cost of all. You need to be in compliance with the newer codes a metal vent pipe or corrugated metal flex pipe installed to the outside of the house. No longer are plastic dryer vent hoses allowed. They need to simply drill a four inch hole on the outside wall of the house where the foundation meets the structure.
Assuming you have at least 18 inches of exposed foundation wall on the outside of the house and your home is not clad in brick this should be a cost factor of around $150 to put this in. No PVC allowed for dryer venting and it does not need to go any higher then then around 18 inches above the ground or at least six inches higher then your average snow fall in your area.
All said in done, a cost of around $1,800-$2,000 should be more in line with the cost to do this job. But remember there are a lot of variables in this. It all depends on available electrical, water and drain connection points. Btu that cost seems a bit high to me. I would continue to shop around on this as well as consider perhaps another location to put the machines if this is causing the price to go up so high.
Wow...thank you for your prompt reply and thorough explanation, just what I was needing-will get another estimate b4 proceeding-thanks again