Hi,
LEM cannot collect logs via WMI & the template mentioned above is a Server & Application Monitor template. SAM can monitor your Kaspersky server via WMI & can monitor services, processes, TCP port availability, etc.
LEM can collect logs from your Kaspersky server. The LEM connector is applied to the agent & connects to your Kaspersky database to collect the logs. Have up you configured the connector correctly in terms of database instance name, port, username/password, etc?