Niko, what do you mean exactly by a ‘personal webserver’? Do you mean an online external private web site? Or do you mean an internal device (inside your home) such as a Synology Network Attached Storage (NAS) DiskStation (or something similar)?
The ‘WiFiLogger’ send its data wirelessly directly to the (home/internal) network router (and not to a specific device such as a computer and/or a DiskStation). If the ‘webserver’ has access to the network, then the ‘webserver’ has access to the data from the ‘WiFiLogger’.
I have a Synology NAS DiskStation that is connected to my home/internal network router (the same home/internal network to which the ‘WiFiLogger’ is wirelessly connected) - the NAS can access the data from the ‘WiFiLogger’ by simply looking at the assigned IP address and the port number of the ‘WiFiLogger’.
The data from the ‘WiFiLogger’ can also be sent to an FTP and/or MQTT server - two files are then produced by the ‘WiFiLogger’: ‘realtime.txt’ and ‘wflexp.json’. Obviously, the ‘webserver’ will need code to extract the data from either of those files.
Unfortunately, I have not tried the FTP/MQTT server option as I had no need for it. 
If interested in finding more about the FTP/MQTT server option, please, let me know - give me a few days and I could try setting the FTP/MQTT server option and check/test the results… 