I am happy to be corrected, but I do not think repetitive motion (read: rowing) necessarily leads to repetitive emotion injury. The latter, development of a problem like tendinitis, may arise out of repetitive motion some of the time. But I suggest that the injury does not result from the motion or the repetition itself, but rather from something about the motion that is stressful to that part of the body - and which the person making the motion is not handling properly.
For example, in the spring when a rower begins to row outside after a winter indoors on the rowing machine, one key change is having to feather and square every stroke, which requires quick back and forth movements with the hands/wrists/forearms. And it may be in colder weather, possibly another aspect of stress on the part of the body newly in use. The combination of a new motion, back and forth and rapidly repeated, may result in strain on tendons in the wrists. However, all that is needed to avoid the tendonitis is to work into it (rowing with feathering) gradually. Make the first few rows a little shorter, fewer strokes, lower rating, less pressure/pull on the arms. Build up the distance and number of strokes you take and allow the wrists to strengthen, relax, acclimate to the new motion over a period of days.
If repetitive motion such as the rowing stroke always or inevitably caused repetitive motion injury, every rower would suffer from it. And given the use of the whole body, the RMI conditions would be pervasive - hands and arms, shoulders and back, hips and knees.
When done in moderation, one aspect of which may be the phasing in of more challenging work or motion, rowing need not result in injury, from repetitive motion or otherwise.