Version checking options control how often MultiPing checks to see if there is a new version available. This requires an internet connection. If you're using a proxy server, then entering your proxy server information here will allow MultiPing to check for a newer version of itself.
Please keep in mind that this does not affect the way Ping requests are sent at all. Proxy servers do not support Ping requests, so you'll need to open up your firewall to allow outbound ICMP echo requests and returning ICMP echo replies.