OpenBSD now has a 64-bit time_t on 32-bit systems. time_t was always 64-bit on 64-bit systems on OpenBSD.
IMO this is one of the things that is being mostly ignored. Back around 2000, many people were saying things along the lines of, "we'll all be on 64bit or larger systems by 2038, so it will solve itself". Many more people have ignorantly joined that line of thought, since almost all mainstream cpu's are 64bit now. That said,there are still a large number of 32bit cpu's being made (like almost every android device CPU there is, and most Apple iPhone/iPad things, and many of the chromebooks out there):
All ARMv7 based CPU's, such as:
* Qualcomm Snapdragon S4 (nexus 7)
* ARM Cortex-A9 (ex. Exynos 4210 in Galaxy Tab 3)
* ARM Cortex-A15 (ex. nvidia tegra K1 in NVIDIA SHIELD; Galaxy Tab 4 and S, ASUA Chromebook C201 with Rockchip 3288)
Apple mobile products:
* Apple A4 (ARM Cortex-A8): iPhone 4, iPod Touch (4th gen), Apple TV (2nd gen)
* Apple A5 (ARM Cortex-A9): iPad 2, iPhone 4S, iPod Touch (5th gen), iPad mini
* Apple A6 (ARM Cortex-A15): iPhone 5
Some notable 64bit exceptions:
* Apple A7 (ARMv8-A): iPhone 5S
* Apple A8 (ARMv8-A): iPhone 6 and 6 Plus
* Apple A8X (ARMv8-A): iPad Air 2
* Exynos 5433: Galaxy Note 4 (but it only runs in 32bit mode)
* Exynos 7420: Galaxy S6 and S6 Edge
* NVIDIA Tegra X1: ... I don't know if this is in anything yet.
The work that OpenBSD did needs done everywhere. 32bit systems need to have a 64bit time_t.
Also, like y2k, there will be LOADS of data storage issues - databases that need tables altered, etc. Unlike the printed date, it will be far more difficult to make assumptions about the values based on proximity to the current date (ie. 9/11/01 was considered to be 2001, but 7/4/48 was considered 1948). time_t was a signed 32bit int, so it will wrap around to negative which has an poorly defined behavior.
Anyway.. the point that I assume is in the article is probably about future dates (and timestamps). Those will be major issues far before 2038 itself arrives (just like scheduling systems in the late 90's had to be the first to be updated).