An issue of timing: The original rules…
Pathfinder Player Companion: People of the North (Jan. 2013) presents the fighter archetype viking (24-5) and, so far as I can tell based on the list of references in People of the North's, at the time Ultimate Combat (Aug. 2011) contained the most recent rules for archetypes:
If an archetype replaces a class feature that is part of a series of improvements or additions to a base ability (such as a fighter’s weapon training or a ranger’s favored enemy), the next time the character would gain that ability, it counts as the lower-level ability that was replaced by the archetype. In effect, all abilities in that series are delayed until the next time the class improves that ability. (23)
(This information—identical but unsourced—is on d20PFSRD in the section on Class Archetypes on Archetype "Stacking.")
Given the differences in the archetype's class features' presentations and because the fighter archetype viking doesn't specify otherwise, it appears that viking archetype's extraordinary ability shield defense should, based on the rules available at the time, only delay the viking fighter's first iteration of the extraordinary ability armor training until level 7 (and the second iteration until level 11 and the third until level 15).
That is, contrast the extraordinary ability shield defense with the extraordinary ability berserker that seems to outright annihilate the fighter's weapon training at levels 5, 9, 13, and 17. (Presumably that's what's meant when the special ability berserker description says weapon training 1, 2, 3, and 4.)
...And the newer rules…
However, the Advanced Class Guide (Aug. 2014)—the earliest mention of the following rules I could find—, includes the above rules also includes the following:
If an archetype replaces a class feature that has a series of improvements, but it does not list one individual improvement, that class feature replaces the entire class feature and all of its improvements. For example, if a class feature says that it replaces trap sense without mentioning a specific bonus, it replaces all of trap sense. (74)
(This information—identical and sourced to the Advanced Class Guide—appears on d20PFSRD under the heading Hybrid Class on Selecting Archetypes for each class's archetypes, such as the shaman's archetypes.)
Thus, if the above rules are applied retroactively to the viking archetype's class features, the viking archetype's extraordinary ability shield defense indeed does completely replace the entirety of the fighter's extraordinary ability armor training (and, not inconsequentially, makes the note weapon training 1, 2, 3, and 4 on the viking's extraordinary ability berserker all the more superfluous).
"Why didn't Paizo issue errata for the viking archetype?"
Paizo policy is not to issue errata for its smaller works. All of the big, high-volume books are subject to errata when reprinted, but the littler books often never get reprinted, so there's no need to look at them again. Once such a smaller book's sold, the consumer's pretty much on his own. (This factoid's mentioned several times with a quick search of Paizo's site.) A list of texts with errata as of 2016—listing People of the North as having received none—is available here.
Note that the d20PFSRD's table of fighter Archetypes and Alternative Class Features applies these later rules retroactively, having the shield defense replace armor training throughout the viking fighter's career. But also note that the d20PFSRD's table is third-party rather than official material, compiled (and, in this case, interpreted) by folks reading the same material we are.
...And what this GM would do to resolve the issue
This GM would go with the more generous reading, granting the viking fighter the shield defense ability at level 3 and the armor training ability at levels 7, 11, and 15. The extraordinary ability armor training is a tiny bit of help when the fighter needs so much more, and it won't be until level 11 (when a wizard's been casting for 2 levels teleport) that the fighter can take instead advanced armor training. A strict GM that nonetheless allows the viking to have both shield defense and armor training might likewise eliminate the ability of the viking to take any advanced armor training (the Armor Master's Handbook being unavailable when the viking archetype was published), but this player would argue that being a fighter is already difficult, and opening up to the viking a few such special abilities aren't going to break the game.