My friend and I just took this tour in April. We were in Barcelona 4 days prior to tour and 3 days after in Madrid. A step counter showed we actually walked more on the days on our own.
I think perhaps the strenuous is because of the amount of stairs. Some metro stops have steps going down. Usually there are escalators going up, but we did come across some that were not working. Some metro and train stations only had steps that I could see. I think there are elevator options in most metro stations, but you have to go looking for them. As a tour group uses the metro, you are hurrying along and the group probably isn't going to wait for other exit/entrance options. In museums we used stairs usually between floors. Park Guell had a long flight of stairs at the end to return to bus. In various places, frequently there were not handrails on the stairs.
When walking with the tour group on streets, there was the expectation that you would stay close together and be ready to cross the street together when the walk signal indicated 'go'. Of course everyone waited for those that need to wait for the next walk cycle. Street walking wasn't strolling.
I've been on three other RS tours and think the Greece tour was more strenuous.