You have some different ways of doing this.
1. Take a look at the track_data & track_info tables.
You need the positions, and not necessarily the NMEA data? Take a look at the database. There is one table called track_data which stores a position every 10 seconds (in build 62). How often and by what criteria can be configured. And track_info which is a "header" for each track.
2. Use the GpsGate Protocol to get a stream of NMEA data
GpsGate.com Client SDK contains a protocol on how to get a live NMEA stream of data from GpsGate Server. It is TCP/IP based, or you can use .NET assemblies found in the SDK or an ActiveX. Download here, more docs in the download:
3. Store data to NMEA log files on server
This feature is coming in the next service release of GpsGate Server. It will allow you to save all incoming NMEA data to separate files on the server for each user.