I AM Dutch (meaning I'm from the Netherlands) so I have access to some really good info on this aircraft.
It was indeed meant as a 'jachtkruiser' which roughly translates into a zerstörer (destroyer). It was intended to perform long range fighter, reconaissance and light bomber duties and was of mixed construction with fabric over steel tube fuselage and wooden wings. When Germany invaded the Netherlands on 10 May 1940 most were destroyed on the ground, and many planes commandeered by the military (originally built to foreign contracts) were yet without armament and other equipment.
The G-1 was apparently easy to fly and maneuverable and could dive very fast although it was underpowered and quite a bit slower than the Bf109 and 110. It was built in two versions, the Mercury powered 'big' version, also known as the G1 'A' version and the 'small' Wasp powered 'B' version meant for export. I don't know for whom they were intended though, have to look it up. There seems to have been a fair amount of interest in the plane though, for example by the Finns (who already were using Fokker D-XXI fighters).
Dutch pilots however preferred the XXI, which was smaller, simpler and only slightly slower and most importantly much quicker to scramble. I also heard that the G-1 carried quite a big amount of fuel in its wingroot tanks which were unprotected and would easily burn when hit in combat. After May 1940 production continued for the Luftwaffe which used them as advanced trainers for the Bf-110.
After the war Fokker resumed production with highly succesfull small airliners (F-27 & F-28) and also built a long line of fighters for the Dutch Airforce, Meteors, Hunters, Sabres, Starfighters and F-16's, although the company has gone bankrupt and has broken up, no new Fokkers anymore

Therefore, the G-1 remains as the most advanced Dutch fighter ever built!