A Smart TV can connect straight to the internet to access various features like channel guides, websites and streaming content. So you could say that a streaming media player turns a regular TV into a Smart TV since it pulls content from the internet to display on the TV.
However, if you have a Smart TV, you may want to use a separate player as TVs often don’t support as many apps as the players do. So no, you don’t need a Smart TV to use a streaming player. To conclude, it depends on your need.