You are correct that you can just delete the log files from the database, the suggestion to archive them is so you can refer to them should you have any issues with your design. There is no built in mechanism to do this via the tools you may simply move them from the project to another location on your hard drive or off-line storage. The log files that Server Monitor is reporting on are those used by the iCDB database so they're log files under database/cdbsvr/log, database/cdbsvr/dbcheck, database/cdbsvr/dbupgrade, database/cdbsvr/PIMlog and database/cdbsvr/plog. You may also clean up the log files under CES/LogFiles though these are not monitored or reported by Server Monitor.
You can also disable this warning in Server Monitor from the Settings - Issues - Server Processes window or make the threshold bigger by editing the Server.cfg file in your local writable WDIR directory - $WDIR\iCDB\Server. You can uncomment the line LogFilesWarningSize_MB = xx and make xx as large as you consider reasonable.
In the next release the iCDB Project Backup utility will have an option to clean up the log files for the project.