The product is made by Polywarm, and will be MVP (as are dozens of other fabrics), so is also a semi permeable membrane like gore tex is, but it is not gore tex, and may not be as good as gore tex either. To be actual gore tex it would need to be made by
'W L gore' (hence-gore tex).
It is also worth noting that gore tex is not the best MVP fabric by a long way, and has not been for quite a few years, The current market leaders (which are way better) include fabrics like E-vent. Since first coming onto the market roughly thirty years ago, gore tex has improved, but still uses roughly the same two or three layer construction and technology.
Whatever system the bivvy bag you have uses, it always has to be remembered that any MVP fabric can only 'work properly' when it has its own micro climate, so if the bivvy bag was wide open, then the pressure will be the same on the outside as on the inside, so there will be no force to push out your bodies vapour. I only mention this, as sometimes students wonder why they get more sweaty in their MVP jackets (during moderate activity), when they are undone, as opposed to ziped up lol.
Edited to add.
Just as sapper says, you can put paper inside, and spray it. If you do this, it may be better to to use cardboard, as not only will the leaks show more easily, but as the card board is stiff, you will be able to identify exactly where any leaks are (as the leak can grow/spread on the inside face of the fabric. Alternatively, turn the bivvy inside out and spray it. And leaks will be seen instantly, and can be marked with pen/marker while they are still less than 1cm square (for better accuracy). For patching the inside or outside, I use seam grip (not seam sealer) or evostick, with a patch of similar waterproof material to the item in question.