  Compact elliptical galaxies (CEGs) are candidates for local analogs of the
high-redshift "red nuggets" thought to represent the progenitors of today's
early-type galaxies (ETGs). To address whether the structure of the dark matter
(DM) halo in a CEG also reflects the extremely quiescent and isolated evolution
of its stars, we use a new $\approx 122$ ks Chandra observation together with a
shallow $\approx 13$ ks archival observation of the CEG Mrk 1216 to perform a
hydrostatic equilibrium analysis of the luminous and relaxed X-ray plasma
emission extending out to a radius $0.85r_{2500}$. We examine several DM model
profiles and in every case obtain a halo concentration $(c_{200})$ that is a
large positive outlier in the theoretical $\Lambda$CDM $c_{200}-M_{200}$
relation; i.e., ranging from $3.4\,\sigma - 6.3\, \sigma$ above the median
$\Lambda$CDM relation in terms of the intrinsic scatter. The high value of
$c_{200}$ we measure implies an unusually early formation time that firmly
establishes the relic nature of the DM halo in Mrk 1216. The highly
concentrated DM halo leads to a higher DM fraction and smaller total mass slope
at $1R_e$ compared to nearby normal ETGs. In addition, the highly concentrated
total mass profile of Mrk 1216 cannot be described by MOND without adding DM,
and it deviates substantially from the Radial Acceleration Relation. Mrk 1216
contains $\approx 80\%$ of the cosmic baryon fraction within $r_{200}$. The
radial profile of the ratio of cooling time to free-fall time varies within a
narrow range $(t_c/t_{\rm ff}\approx 14-19)$ over a large central region ($r\le
10$ kpc) suggesting "precipitation-regulated AGN feedback" for a multiphase
plasma, though presently there is little evidence for cool gas in Mrk 1216. The
properties of Mrk 1216 are remarkably similar to those of the nearby fossil
group NGC 6482.
