The repair language was discussed by Republicans during their closed-door policy retreat in Philadelphia last week as a better way to brand their strategy. Some of that discussion flowed from views that Republicans may not be headed toward a total replacement.
So why are they doing this?
I think your linked article already mentions the relevant point.
As the article notes, 75% of Americans do not want to repeal the Affordable Care Act, at least not without a proper replacement:
Using the word repair “captures exactly what the large majority of the American people want,” said Frank Luntz[.]
While the ACA in its current form is rather disliked, polls show that people do not want to repeal it altogether, but instead improve it. This isn't really a new development either, see for example this poll from 2014 (30% for repeal, 52% for improvements). The main reason for this is likely that people do not want to lose the benefits gained under the ACA (no exclusion for pre-existing conditions, larger coverage, etc).
Another reason may be that Republicans do not have an actual replacement plan. The ideas they do have will likely be rejected by most other Republicans and have been described as unworkable.
Three factors plus political calculus lead to the change in strategy.
The factorsIf the GOP were to repeal the ACA, they would politically own the result. A repair strategy is less risky than a repeal strategy because the GOP will not own the defects in the system (as they would after a repeal) and, instead, they can continue repairing the ACA into future election cycles.
It's partly semantics and partly implementation strategy.
The ACA isn't a single provision, it's a maze of interlocking pieces that has hooks in every aspect of life in the US. It can't simply be terminated or replaced overnight because it would be like trying to unscramble an egg. When all is said and done, there will be a system in place with differences from the ACA. As the ACA, itself, demonstrated, trying to implement change of this scope and complexity in a single step leads to unanticipated problems.
Any legislation dealing with the subject will have massive overlap with the ACA, and the objective has always been to retain certain beneficial features, like providing for pre-existing conditions and allowing young people to stay on their parents' plan. So even a complete replacement will have certain similarities.
No change can be implemented overnight because of the lead times required to implement them. No matter how change is accomplished, the result will be a blur of old and new that will stretch over a period of more than a year.
In the meantime, changes need to be made because the ACA is crumbling under it's own weight. Some things in the current plan need "repair" to survive until more permanent structural changes are in effect.
Beyond that, it is simply good business practice to implement change incrementally to the extent practical. Some structural elements have dependencies that require concurrent implementation. Other pieces that have turned out to be problematic can be individually fixed, at least temporarily. There is also a balancing act of implementing changes in a deliberative, and to the extent possible, incremental manner, vs. having a stable and predictable environment for all of the players.
Getting to the finish line will be a combination of immediate patches and fundamental changes. The election changed the landscape for what can be changed and how that change can be accomplished. Given that, efforts have been refocused to reflect that new reality. That includes both the "what" and the "how".
The objective for the end result is fundamentally unchanged, although the political realities may allow minor differences from what was contemplated during the Obama administration. Now that Republicans are in a position to actually implement substantive change, one of the first steps is to figure out the best way to accomplish that. Strategy details have moved from campaign rhetoric to implementation plans, so refinement is to be expected.
There is also an element of encouraging bi-partisan participation, so terminology like "repair" is more palatable to Democrats. And I suspect that current calls for "repeal" by some Republicans is part of the posturing and negotiating dance.
