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The reason that we see a ring at all is because the plasma surrounding the black hole is "geometrically thick, but optically thin" at the 1.3 mm wavelengths used in the observations. What this means is that mm-waves are generated by fast-moving electrons in the plasma that is being accreted onto the black hole and the plasma exists over the whole of the region imaged (and beyond), but that most of the emitted light will escape self-absorption.

This matters greatly near a black hole, because the densest plasma will be nearest the black hole but any light that is emitted and heads inside the location of the "photon sphere" at $1.5 r_s$ will end up in the black hole, possibly after orbiting many times and is lost. Light emitted outwards from dense plasma inside or at the photon sphere may orbit many times and then escape from the edge of the photon sphere. Light emitted just outside the photon sphere can be bent towards us on trajectories that graze the photon sphere.

Inside the ring is relative darkness. There is light coming towards us from this direction - from plasma between us and the black hole, but it is much fainter than the concentrated light from the photon ring. Much of the light that would have come to us from that direction has fallen into the black hole and hence it is referred to as the "black hole shadow".

EDIT: The observed ring is not the accretion disk

A set of simulations were done as part of the analysis of the EHT image and are described in paper V of the EHT M87 series. Fig.1 of this paper shows an intrinsic images (i.e. prior to blurring with the instrumental resolution) that provides a reasonable fit to what is seen (see blow). In all cases the emission is dominated by the photon ring and the direct contribution of the accretion disk/flow is much lower.

The reason that we see a ring at all is because the plasma surrounding the black hole is "geometrically thick, but optically thin" at the 1.3 mm wavelengths used in the observations.This means that mm-waves are generated by fast-moving electrons in the plasma that is being accreted onto the black hole and the plasma exists over the whole of the region imaged (and beyond), but that most of the emitted light will escape self-absorption.

This matters greatly near a black hole, because the densest plasma will be nearest the black hole but any light that is emitted and heads inside the location of the "photon sphere" at $1.5 r_s$ will end up in the black hole, possibly after orbiting many times, and is lost. Light emitted outwards from dense plasma inside or at the photon sphere may orbit many times and then escape from the edge of the photon sphere. Light emitted just outside the photon sphere can be bent towards us on trajectories that graze the photon sphere.

Inside the ring is relative darkness. There is some light coming towards us from this direction - from plasma between us and the black hole, but it is much fainter than the concentrated light from the photon ring. Much of the light that would have come to us from that direction has fallen into the black hole and hence it is referred to as the "black hole shadow".

The observed ring is not the accretion disk

A set of simulations were done as part of the analysis of the EHT image and are described in paper V of the EHT M87 series. Fig.1 of this paper shows an intrinsic image (i.e. prior to blurring with the instrumental resolution) that provides a reasonable fit to what is seen (see below). In all cases the emission is dominated by the photon ring and the direct contribution of the accretion disk/flow is much lower.

The Figure above is from paper V of the EHT data release on M87. It shows the observations (left) a General Relativistic simulation (center) and the same simulation blurred by the instumental resolution of the Event Horizon Telescope (right). The dominant feature is the photon ring. A weak disk contribution (or rather inflow from the disk) is seen in the simulation, but contributes little to the observed ring seen in the observations.

A direct quote from that paper:

The central hole surrounded by a bright ring arises because of strong gravitational lensing (e.g., Hilbert 1917; von Laue 1921; Bardeen 1973; Luminet 1979). The so-called "photon ring" corresponds to lines of sight that pass close to (unstable) photon orbits (see Teo 2003), linger near the photon orbit, and therefore have a long path length through the emitting plasma.

The Figure above is from paper V of the EHT data release on M87. It shows the observations (left) a General Relativistic simulation (center) and the same simulation blurred by the instumental resolution of the Event Horizon Telescope (right). The dominant feature is the photon ring. A weak disk contribution (or rather inflow from the disk) is seen in the simulation, but contributes little to the observed ring seen in the observations.

EDIT: The observed ring is not the accretion disk

The apparent radius of something residing in a Schwarzschild metric, when viewed from infinity is given by $$ R_{\rm obs} = R \left(1 - \frac{R_s}{R}\right)^{-1/2}\ ,$$ where $R_s$ is the Schwarzschild radius $2GM/c^2$.

This enlargement is due to gravitational lensing and the formula is correct down to the "photon sphere" at $R =1.5 R_s$.

Most of the light in the EHT image comes from the photon sphere. It is therefore observed to come from a radius $$ R_{\rm obs} =\frac{3R_s}{2}\left(1 - \frac{2}{3}\right)^{-1/2} = \frac{\sqrt{27}}{2}R_s\ .$$ This is almost precisely what is observed if the black hole has the mass inferred from independent observations of the motions of star near the centre of M87.

By contrast, the accretion disk would be truncated at the innermost stable circular orbit, which is at $3R_s$ and would appear to be at $3.7R_s$ as viewed from the Earth (or larger for co-rotating material around a spinning black hole), significantly bigger than the ring that is observed. So we might expect disk emission to come from further out.

Nevertheless, there is inflow from the disk and General Relativistic simulations involving magnetic fields do show some emissivity in a broader disc-like structure around the black hole.

A set of simulations were done as part of the analysis of the EHT image and are described in paper V of the EHT M87 series. Fig.1 of this paper shows an intrinsic images (i.e. prior to blurring with the instrumental resolution) that provides a reasonable fit to what is seen (see blow). In all cases the emission is dominated by the photon ring and the direct contribution of the accretion disk/flow is much lower.

The Figure above is from paper V of the EHT data release on M87. It shows the observations (left) a General Relativistic simulation (center) and the same simulation blurred by the instumental resolution of the Event Horizon Telescope (right). The dominant feature is the photon ring. A weak disk contribution (or rather inflow from the disk) is seen in the simulation, but contributes little to the observed ring seen in the observations.