That looks like a bit of a hoax. Researching this, the bike went through many changes after its initial invention (from big wheels to a big and little wheel, to 3 wheels, to even helping grant women rights!), but this was not a norm during the war. Yes, during WWII, there was a rubber shortage since the Japanese captured a principal rubber producing area in the Far East in 1942, which eliminated sources of 90% of the world's rubber production (source: Wedt, Paul. The Control of Rubber in World War II. The Souther Economic Journal. January, 1947.). This forced the US to create a synthetic rubber. There were also stories of people putting newspapers in their tires of vehicles to make them last as long as possible, since originally it was extremely difficult to get new tires...
TL;DR There was a rubber shortage during WWII, but it didn't make people ride steampunk inspired bicycles
As a Dutchie I can tell you that during WW2 the germans took the good bikes from the Dutch people. When the tires of the other bikes would break, they would use anything they could to still keep the bikes riding. There was no monney for or acces to synthetic rubber. They used wood or nothing at all and just ride the bike.
TL;DR There was a rubber shortage during WWII, but it didn't make people ride steampunk inspired bicycles