I suspect that the left needle position is the default for your machine. Looking at the photo here, it certainly looks like that is the case. (What a nice looking machine!)
Brother Riviera 1681 Sewing Machine eBay If you watch this video during the straight-stitch segment, you will see the needle is in the left position.
https://www.youtube.com/watch?v=Qflwon_EVSU
Some of the older machines were made this way--I have an old Nelco that is left default--tough machine, sews almost anything! Unfortunately, if you want a center-needle machine, you would have to buy something else. (Forget about any of the new plastic machines on the market. This Brother will out-sew and outlast them any day of the week.) On the other hand, this is probably a great machine, and once you get accustomed to the left needle, you'll be able to do anything that a center needle machine can do.
FWIW, a sewing machine whose bobbin loads on the left is usually left needle default.
Manual:
http://www.sewingshop.com/1681MANUALPDF.aspx
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