It's a 'dumb' splitter because all it does, as it says on that page, is:
"When virtual serial ports are opened by communications applications correspondingly, data from the physical COM port is sent to all opened virtual COM ports simultaneously. And vice versa, data from each communications application written to a virtual COM port is sent to the physical COM port."
It doesn't understand the Davis communication protocol. Having more than one program talking to the station at the same time will thoroughly confuse it. It would only work if only one program was controlling the protocol and the all the other software was able to just listen and recognise the responses and act on them. I don't know if there is any existing software for Davis stations that will work in a 'passive' way like that. I imagine it would be quite difficult to write software to do that.