It's a stepped linear emission that mimics an inverse exponential emission. You can even see it in that chart if you expand it. Between the halving periods the emission is constant.
If you zoom in enough, you won't see these exponential steps. If you were able to zoom out completely, you'd see _only_ the exponential function. Bitcoin's emission is an exponential function (dropping exponentially), the fact that there is some time period between these exponential steps does not make it non-exponential. This would have been obvious if the halvings were every 30 minutes, but it's much less obvious when the "in-between step interval" is 4 years.
The block subsidy is constant between halvings. And is thus a step function.
But "emission" refers to cumulative block subsidies. And thus is piecewise linear, with 34 pieces of exponentially decreasing slope, the last one ending up flat.
[1] https://medium.com/amberdata/why-the-bitcoin-supply-will-nev...