If these files are definitely RTF files, though are opening in Word, you can set it up so they always open in WordPad to save you having to use the right click option, by doing the following.
Double Click 'My Computer' and choose Tools > Folder Options and click the 'File Types' tab. This may take a moment to load. Once the list is loaded the file extensions should be sorted alphabetically, and if you scroll down and find the 'RTF' extension. Once highlighted it will probably tell you below that it is set to open with Word. To change this hit the 'Change' button, and in the list of Programmes that appears highlight WordPad. Ensure the tick at the bottom is ticked that says 'Always use the selected program to open this kind of file'. Click OK
Now, any time you double click an RTF file it should open in WordPad, and also the Icon for any RTF files should change back to the WordPad Icon.
As for why this happened, you mentioned a re-install. If software was re-installed it is possible whoever did this automatically selected that RTF was one of the file types Word should associate with, as this is the usual format.
Hope this helps.
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