The film takes place in 2565.
A fanciful rendition of what the future in space might look like. When this short was released, the space race was in full swing, with a manned moon landing just two years away.
There are some winks at the popular sci Fi TV shows of the time. But the robotic animals and vehicles have since become part of mainstream technology today (2021).
The ending, where the characters are sent back in time due to an interference in the space-time continuum, has been explored in many Sci Fi works. Star Trek addressed it several times, in different series and films, for example. And the TV comedy "It's About Time" centered on this, with hilarious, if improbable, story lines.
Both Tom and Jerry silently break the fourth wall in this short.