Although the article and the official announcement attempts to paint a conciliatory tone, and justify the reason on the growing international nature of the church (scouting was only available to members in the United States and Canada, but the Church membership has moved beyond those locales), and more fairness in funding between programs for young men and young women (which must be at the national level, because it doesn't show up at the local level), that explanation seems likely to only mollify the progressives in the Church. It stands to reason that the decision was mostly a result of the backlash among Church members when the BSA decided to allow openly gay leaders, to "welcome" gay scouts, and, most recently, allowing transgender "boys" to join and considering opening certain aspects of scouting to females. Quite simply, the BSA has converged, moving from an organization intended to mold boys into men, to just another organization led by social justice warriors. And it is reflected in it dropping certain basic "scouting" merit badges, such as tracking, and the adoption of merit badges centered on politically correct topics. To paraphrase from the Bible, the BSA is salt that has lost its savor.
The impact of this decision will probably not be significant at first. The Church has indicated that it will pay dues for all of its youth through 2018, so there won't be an immediate financial impact on the BSA. (I'm old enough to remember when the individual members were required to pay the dues for their children). Although the 14 through 17 year old youth may have continued into Varsity and Venture Scouts on paper, I have never seen or heard of any activities for Varsity and Venture Scouts in any of the wards (the local congregations) that I've attended--this with my oldest having been active in scouting and who would have welcomed continued activities. Thus, if this holds true throughout the Church, there will probably be little impact on BSA operations.
The long term impact of this decision, however, will probably be the demise of the BSA. The LDS Church was the BSA's cash cow, and I expect that the Church will withdraw from the other scouting programs for the 8 to 13 year old boys in the coming years. Besides the funding that comes directly from the Church, there are also the annual fundraising ("Friends of Scouting") that nets additional monies from individual members. In addition, other churches have been vacillating on whether to leave the BSA because of its shift to the left, and I would not be surprised if the Catholic Church and some of the larger Protestant denominations also left (we've already seen an exodus of Evangelical churches).
Will the LDS Church replace it with anything better? It is hard to tell. It often seems to me that Church activities are not selected or approved based upon what the members want or need, as by what risk managers find acceptable or what outsiders may think. I note, as an example, that the list of activities for 14 to 18 year old youth includes fishing, scuba diving, canoeing and camping, but not anything related to hunting, trapping or firearms, even though the latter activities are the safer ones.
Other articles on the topic from NPR, The Los Angeles Times, and the Salt Lake Tribune.