Update: Due to the aforementioned work-related issues, I haven't had time to worry about this situation for a while, but it's time for an update.
While the dryer appeared to be working at first, a lot of lint was collecting inside the dryer, clothes were taking a very long time to dry, and there was a faint burning smell after the dryer had been on for a while. Of course, I thought that the hose wasn't connected (remember that they hadn't plugged it in, so this isn't a big stretch). Due to the tight confines of the space and the weight of the stacked units, I can't move them to check myself. It took three guys to move it into place during install. So we called to have someone take a look, explicitly telling them to send at least a couple guys because they'd have to move the units to check the hose. They set up an appointment for this Wednesday morning from 8-12, so I took the morning off. I sat in the living room for four hours waiting and no one showed up - not even a phone call. I e-mailed Evadman just before I left to let him know what was going on. So at 12:15, I left to go to work. Right around the same time (12:07), the repair guy called my wife to let her know that he was running behind. She told him to call me, which he never did.
Evadman called me right when I got to work. He said the tech was in Affton, MO (about 20 minutes away) and was two stops behind. I told him I was at work but that my wife might be able to get home by 1:30, so he made a note that the guy should show up around then. The tech called me at 1:15 to say he'd be there in 15 minutes and asked what was wrong. Immediately after I told him, he said that it sounded like the exterior vent (the one that takes the exhaust out of the house) was clogged and that he wouldn't be able to do anything about it. I told him that we had already cleaned it because we had had that problem previously and that it must be the hose. He said if it's the hose, it's a delivery problem and he still wouldn't be able to do anything. At this point, I wanted to say, "Isn't this just a Sears problem?" but I know an exercise in futility when I see one.
My wife let him in around 1:30. He walked up the stairs, turned on the dryer, smelled the burning smell, and said again that it must be the clogged exterior vent, then left. He never looked at the hose or anything else. Apparently he had made his diagnosis over the phone and didn't even need to show up to know that he was right. Must be nice to be so talented. He told my wife that we would have to get it professionally cleaned to solve the problem, which was obviously ridiculous since the old dryer was working perfectly through that same vent. For the sake of tradition, my wife cleaned the vent again and threw some wet clothes in to try it out with - surprise, surprise - the same result as before.
When I got home, I took a look at the vent. I am a lot taller, so I could reach it and put my hand next to it to check for air flow. There was just about no air flow, so I tried my hand at cleaning it. My wife is a cleaning machine apparently because I could have eaten out of the vent at that point. Again, I hoisted my wife over the dryer, this time with a flashlight (it's dark back there!) so she could get a look at the hose. Rather than not being attached, the metal hose was much too long for what they were doing and had basically been mangled when they pushed the dryer into place when installed. I stuck my arm over the dryer to take a
picture for ATOT.
I forwarded the picture to Evadman, who had the delivery people call my wife. She was at work and couldn't answer, so I called the number they left on her voicemail and talked to "Veronica," who had a nice Indian accent.

I explained the problem and she put me on hold to "go on Sears.com" to figure out what part I was talking about. After a few minutes, she informed me that washers have hoses but dryers only have cords. Was it the cord that needed replacing? I tried explaining again that it's a metal hose, or that maybe it was called a duct, that comes out of the back of the dryer, but she didn't get it. She said she would schedule a repair tech to come out and take a look at it. I calmly explained that we already tried that, and that we needed at least a couple guys to move the thing to replace the hose. She scheduled a delivery team to come out some time on Monday (exactly four weeks after the original delivery date) to, "look at what's wrong, then order the part." I am now supposed to get yet another automated call telling me when the delivery is supposed to take place on Monday.