Verifying the game cache allows FFXIV to download any missing/damaged/corrupt files. And Steam has a way to solve this problem. If there are some game files damaged/corrupted or missing then the Steam client would show the error message. This solution for the user who is playing the FFXIV on the Steam client. If the error is not solved, move to the next solution. Wait for 5 minutes and then restart the system.
Restarting the system & router is a simple fix as you are playing online and if there is any problem between the communications then restarting the PC & Router is the best option and starting point in troubleshooting any tech issue. If servers are not offline, then move to the next solution. If so, wait for the time mentioned on the forum to recheck for the game servers to be back online.