The WLL show a light gray line going to a PC. How is this connection achieved?
There is no huge significance to the WLL line being grey. It is a thick solid line to indicate that it is perfectly usable for passing data to a PC program. WLL is a network device, so data is only passed to a PC via a network connection - either WiFi or Ethernet.
However, using a different colour denotes that the data format is completely different from the traditional Davis binary API/format and so can only be used with software that is explicitly compatible with WLL.
The data architecture also differs in other ways, eg with WLL there is no concept of summary or archive/historical data in the traditional Davis sense. AFAIK any catch-up process (eg if the logging program was offline or down for any reason) needs to retrieve the missing data using a Pro subscription at weatherlink.com, rather than from the WLL unit.