I think several Microsoft sowtware from that time workes that way. At least it was the case for Flight Simulator 4, that I received for Christmas when I was 13 or 14. I remember having to type my name and the #SN in order to install it on my parents' SE, and every subsequent installations had my name on them. Actually I long lost the original floppy, box and manual (what a shame!), but the copies of the application I still have lying on different machines still do have my name on them.
By the way, to you guys and Scott in particular, is it THAT important to strictly respect copyright on such old software? Clearly, those three sealed copies of Word have a greater value than opened. Wouldn't it be ok for you (though not strictly ok in terms of copyright law) to keep all three safely sealed, and use one of those copies from abandonware sites?