Hi Joanna and welcome! Little clematis plants really do have weak stems like that and in the spring you'll need to support it with some slender sticks or little stakes. It's too bad that one of the stems broke, probably from rough handling in shipping, but it won't hurt the plant's overall health now. If you can "splint" the little stem to keep it alive until the leaves drop, that's what I'd do just because it would make me feel better.
A couple of toothpicks and some tape? I did this at my daughter's house to a little slip that we had started - her dog broke its one stem in the spring, so I splinted it, and by the end of summer that thing was 4ft. tall. (much more important to keep a stem alive in the spring)
Your little plant looks like it had lots of healthy leaves up until recently. They are going dormant now, so yes I'd expect a clematis to look like that in late September. The important thing now is to preserve the health of the root system. You can expect vigorous new growth next spring from the roots.
I would get busy and plant it out, and water it when the weather is warm. Put a little cage or some stakes around it so it doesn't get stepped on, and when all the leaves have died back, put a good thick layer of mulch over it for the winter. You really don't want the roots 'heaving' out of the ground with freezing and thawing, and you want it to stay evenly moist. Don't give it any fertilizer either. The potting mix it's in probably has a little bit, to support the remaining green leaves.
