"Other mobile chippery firms have experimented with custom application cores, too, but none has made them in the quantities that Qualcomm has. Huawei produces Kirin cores, for example, while LG Electronics and Mediatek have brought us Nuclun and Helio, respectively."
No, not really. All of the above are licensed ARM cores on custom SoCs. Nuclun is Cortex-A15+A7[1], Helio is a high-clocked A53[2], and Kirin has been several things, all of them licensed. [3][4][5]
What Qualcomm and Apple have historically done, and what Samsung is on its way to doing, is using a custom ARM-compatible core design, rather than one licensed directly from ARM Ltd.
[1] http://www.lgnewsroom.com/newsroom/contents/64743
[2] http://www.gsmarena.com/mediatek_helio_is_a_new_family_of_high_end_mobile_chipsets-news-11731.php
[3] http://www.gsmarena.com/huawei_ascend_p7_pops_in_antutu_kirin_910_chipset_gets_tested-news-8345.php
[4] http://www.gsmarena.com/octacore_huawei_kirin_920_chipset_goes_official-news-8720.php
[5] http://www.androidheadlines.com/2015/04/report-huaweis-hisilicon-kirin-930-processor-built-using-28nm-process.html