Translation:There is a chair next to the table.
My JTEs (Japanese Teachers of English) and HRTs (Home Room Teachers) will often say 隣の人（となりのひと）(tonari no hito) when they are specifying that the pair work will be with the student next to them, rather than in front of them. So it can definitely be used for people, though it might be more often used with places and objects.
I just did a quick search and found this really great explanation for the difference between 隣（となり）(tonari) and 横（よこ）(yoko): http://nihongocenter.blog.fc2.com/blog-entry-108.html The explanation is written by a native Japanese and uses a lot of kanji (and it also goes into what "soba" means as well). But this is the basic difference between the two (according to this individual) :
隣（となり）Tonari is used when talking about something that is conceptually close (or viewed as being close), but may not be actually, physically close. It is the thing that is thought of as being the closest to that person. The example they gave was how someone might say, "Korea is beside/next to/near Japan." Obviously, speaking in terms of distance, Japan and Korea are quite far apart. But, in that person's mind/from their point of view, Korea is the closest country to Japan, so saying "Korea is beside/next to/near Japan" is perfectly fine in Japanese.
横（よこ）Yoko is used when someone is talking about something that may be physically far from them, but is shown to be the closest thing in their line of view. The example sentence Duolingo provides here works well to demonstrate this. If you are sitting in a room and you see a table and chair, in your line of view that chair is the closest to thing to the table. Therefore it is next to/besides/near the table.
The Japanese word that relates to physical closeness and has the meaning of "near/close/beside/etc." is 側（そば）(soba). But that is slightly different from "tonari" and "yoko," so I won't go into any more details on that here.
Duo is nobody's friend. Once you understand and make peace with that, you might learn to enjoy it.
Also, shout out to all of the people who have brought the Japanese course up to the level it's at today. It has improved continuously and consistently since it started hatching.
It's explicitly wrong because the table is not a subject.
The location next to the table is given with the location particle に which marks the subjects location. The single chair is marked with the particle が which marks it as the subject.
Although it is logically similar (if a chair is next to the table then it makes sense that the table is next to the chair) this is not the correct translation and the table is not a subject. The place beside the table is being used to mark the location.