Although this is a 3rd party class, we can still use the general rules that the Pathfinder Development Team has established for issues like this one. As far as the Pathfinder Devs are concerned, if a class feature works more or less identically to another (differently named) class feature, they are effectively the same for everything that matters (prerequisites, etc).
See this post from one of the main devs with regards to the Life Oracle "Channel" ability and if it qualifies people for "Channel Energy" feats:
So when the cleric class has a header section called "Class Features" and under that is an entry that says "Channel Energy," and the oracle class has a section called "Class Features" and under that is an entry that says "Channel: You can channel positive energy like a cleric," and the paladin class has a section called "Class Features" and under that is an entry that says "Channel Positive Energy (Su): ... she gains the supernatural ability to channel positive energy like a cleric," those all are intended to work the same way, even though they're not given identical names.
Another sign that the "Firearm Training Trick" should be counted as Grit for prerequisites is the following FAQ, which discusses whether abilities that are renamed in class archetypes still count as their original abilities:
If the archetype ability says it works like the standard ability, it counts as that ability. If the archetype's ability requires you to make a specific choice for the standard ability, it counts as that ability. Otherwise, the archetype ability doesn't count as the standard ability. (It doesn't matter if the archetype's ability name is different than the standard class ability it is replacing; it is the description and game mechanics of the archetype ability that matter.)
I've bolded the section above that matters most to you.
Based on the above two references, I'd say the Firearms Training Trick (which explicitly references working like the Grit class feature) counts as Grit for prerequisites.