Recording more distant birds is always difficult - use a more sensitive mic, or apply more gain, and you also will also boost unwanted noise (ambient and/or equipment self noise). Having a good signal to noise ratio (by being close), is generally the trick to better recordings.
I would advise being cautious about buying a shotgun for your purposes (and particularly the NGT2). Basically, a shotgun is a mic capsule and an interference tube. The tube acts like a filter (better for higher frequencies), so rather than increasing the sound of a bird in front of the mic, it is decreasing sounds off-axis. To pick up fainter sounds, the sensitivity of the mic element becomes important. Looking at the Rode website, the sensitivity of the Videomic Go is stated as -35dB re 1V/Pa (
17.8mV @ 94dB SPL) ±2dB @ 1kHz, whereas the NTG2 sensitivity is -36.0dB re 1 Volt/Pascal (
15.00mV @ 94 dB SPL) +/- 2 dB @ 1kHz. This in fact means that the NTG2 is in fact slightly less sensitive than the VideoMic Go, so will be less good at picking up more distant sounds! Both these mics are in fact not that sensitive. If for instance you looked at the more expensive NTG5, the sensitivity is -23.5 dB re. 1 Volt/Pascal or Better (
66 mV @ 94 dB SPL @ 1 kHz).
A probable advantage of the NTG2 over the Videomic Go, is that the NTG2 has much less self noise, so you should be able to apply more gain, without introducing too much self noise, and therefore running the risk of drowning out a distant birds vocal with noise.
The problem with more sensitive mic capsules, is that they are sensitive to everything, including wind and handling noise. If you go for a sensitive long shotgun, you are probably also going to have to invest in a suspension system and zeppelin type wind shield with dead cat cover. This accessories alone will be expensive.
If you really want to record distant birds, then probably a parabola, if your best option. With a parabola, the dish does actually concentrate the sound in front of the dish - the dish creates additional gain for subjects in the focus. A full size parabola is rather cumbersome and expensive, but there are a few smaller parabolas that may be worth looking at. One is demonstrated in this thread
BirdMic Audio Demo. If you went for something like this, then perhaps you do not need to invest in a recorder, as the system will work with a phone.
I am afraid that I cannot comment on the proposed recorder, as I have never used it. In general though, I think you will see more benefit from the choice of mic than the recorder.