Placing the N on the a-file ignores the principle that one must fight for the center, so it's not surprising that 1.Na3 is not seen in serious play. The claim by Durkin and that analyst of offbeat openings, Hugh Meyers, was that attacking the center can be postponed for a move or two. Meyers pointed out chess is a struggle in which the purpose is to cause problems for the opponent and, while it isn't advisable to play 1.Na3 just to be different, if the move is played with adequate preparation, there is no reason why it can't be considered an option. This is especially true if an opponent does not understand what's going on. But then the same can be said of any opening below the master level. But, the question is, what is going on when white plays 1.Na3? There does not seem to be any clear answer because players like Durkin, Dunst and Goldschmidt all played it differently.
Durkin claimed that he was the first to play 1.Na3 when he played it in the 1948 New Jersey Open and he analyzed it in a booklet titled Knightmare-1, A New Chess Opening, 1.N-QR3, The Durkin Attack. However, in a book published in 1974, Irregular Openings by Tim Harding, he called it the Durkin-Goldschmidt Attack. Harding claimed that a British junior player named Martin Goldschmidt had won some games with it and had his own ideas about how it should be played...namely, 1.Na3, 2.d4 and 3.c4.
While Durkin promoted 1.Na3 more than anyone else, Meyers claimed that Durkin had no clear idea of how it should be followed up! After 1.Na3 Durkin suggested that after 1...e5, then the best moves were, in order of his preference, 2.e3, 2.g3, 2.b3 and 2.c4. Durkin believed that 2.d4 should be playable and on occasion he also played 2.Nc4. After 1...d5, he liked 2.f4, but he also played 2.d4, 2.g3 and 2.Nf3.
So, for Durkin, the move 1.Na3 allowed white to pursue a number of different courses. Because of this, Meyers claimed that Durkin did not invent an opening. What he did was show that 1.Na3 was playable in a variety of settings and according to Meyers, "1.Na3 is not an opening at all."
One thing that Meyers believed Durkin should be given credit for is that he didn't think white had to fear having the N captured by ...Bxa3 and recapturing with bxa3 because Durkin thought that white's two Bs offset the disadvantage of having doubled a-Pawns. In that case Durkin thought white's strategy should be to 1) place the Q on e2, 2) begin central or Q-side operations and 3) get both Rs into play as soon as possible either on the b-file or in the center.
Durkin was of the opinion that if black captured on a3 then white has a ready made plan of attack and the handicap of doubled a-Pawns could be offset by avoiding an exchange of Qs which would be used to defend in the ending; otherwise white would lose a simplified ending because of his inferior P-structure. Meyers questioned whether the willingness of accepting doubled a-Pawns was correct.
Another master who also played 1.Na3 was Theodore Dunst who is also known for what is called in the U.S. the Dunst Opening...1.Nc3. In other parts of the world it's called by about a dozen different names. Dunst successfully played 1.Nc3 against all comers in New York tournaments and correspondence play for many years. When he played 1.Na3 he had his own, and completely different, ideas on how it should be played and observed that after either 1.Na3 or 1.Nc3 the result was usually "trench warfare."
Meyers final conclusion was that in the case of 1.Na3 he found it difficult to name it after anyone!
Here is an example of the trench warfare Dunst was talking about. His opponent, August Rankis (March 29, 1911 - November 2, 1966, 55 years old), was Latvian by birth and shared first with Erik Karklins in the 1947 Latvian-English Zone Championship in Germany. In 1957, he won the New York State Championship with a perfect 9-0 score. He also won the New York State Championship in 1959. In 1965, he won the 5th North American-Latvian chess championship.