There are two different fixes for this issue. The first is simple but takes a bit longer, the second is quicker, but a bit more complicated.
Fix #1: Reinstall
A simple reinstallation should remove the faulting asset files, but the game will need to be redownloaded completely.
In your Steam Library, right-click on Civilization V and select "Delete Local Content".
Then, reinstall the game from the Steam Library listing.
Fix #2: Manually Remove the Problem Files
There are four files that are no longer necessary in the most recent version of the game, so they can be manually deleted from the game's installation directory, if you are comfortable with doing so. This will avoid the need to fully reinstall the game, and will also resolve these errors.
The following files can be safely deleted from their directories. By default, the files will be found in the following: