is Apple still offering this free repair?

Yes, if the machine in question was purchased new less than four years ago. Time has already run out for many of the affected machines, but some are still eligible.

Apple has been very firm about the four-year limit, so if your machine needs the fix, don't dawdle.

As long as you are within 4 years from the date of purchase they are warranted. If not within this limit you might try to talk to someone at Apple as exceptions have been noted on this community forum. Good luck.

The process is fairly straightforward. The tech sticks a flash USB stick in and boots the Mac from it. A test runs automatically. If the Mac is still covered age-wise AND the graphics chipset falls in the defective category, a number pops up onscreen, that the tech uses to order a replacement logic board. Board in hand, an appointment is made for them to do the switcheroo, takes at least a day. At least that's how the Service Providers do it, the Geniuses at the Bar may do it differently

If no number pops up in the test, you're out of luck.