We present a kinematic study of a sample of 298 planetary nebulas (PNs) in the outer halo of the central Virgo galaxy M87 (NGC 4486). The line-of-sight velocities of these PNs are used to identify sub-components, to measure the angular momentum content of the main M87 halo, and to constrain the orbital distribution of the stars at these large radii. We use Gaussian mixture modelling to statistically separate distinct velocity components and identify the M87 smooth halo component, its unrelaxed substructures, and the intra-cluster (IC) PNs. We compute probability weighted velocity and velocity dispersion maps for the smooth halo, and its specific angular momentum profile ({lambda}_R_) and velocity dispersion profile. The classification of the PNs into smooth halo and ICPNs is supported by their different PN luminosity functions. Based on a K-S test, we conclude that the ICPN line-of-sight velocity distribution (LOSVD) is consistent with the LOSVD of the galaxies in Virgo subcluster A. The surface density profile of the ICPNS at 100kpc radii has a shallow logarithmic slope, -{alpha}_ICL_~=-0.8, dominating the light at the largest radii. Previous B-V colour and resolved star metallicity data indicate masses for the ICPN progenitor galaxies of a few x10^8^M_{sun}_. The angular momentum-related {lambda}_R_ profile for the smooth halo remains below 0.1, in the slow rotator regime, out to 135kpc average ellipse radius (170kpc major axis distance). Combining the PN velocity dispersion measurements for the M87 halo with literature data in the central 15kpc, we obtain a complete velocity dispersion profile out to R_avg_=135kpc. The {sigma}_halo_ profile decreases from the central 400km/s to about 270km/s at 2-10kpc, then rises again to ~=300+/-50km/s at 50-70kpc to finally decrease sharply to {sigma}_halo_~100km/s at R_avg_=135kpc. The steeply decreasing outer {sigma}_halo_ profile and the surface density profile of the smooth halo can be reconciled with the circular velocity curve inferred from assuming hydrostatic equilibrium for the hot X-ray gas. Because this rises to v_c,X_~700km/s at 200kpc, the orbit distribution of the smooth M87 halo is required to change strongly from approximately isotropic within R_avg_~60kpc to very radially anisotropic at the largest distances probed. The extended LOSVD of the PNs in the M87 halo allows the identification of several subcomponents: the ICPNs, the "crown" accretion event, and the smooth M87 halo. In galaxies likeM87, the presence of these sub-components needs to be taken into account to avoid systematic biases in estimating the total enclosed mass. The dynamical structure inferred from the velocity dispersion profile indicates that the smooth halo of M87 steepens beyond Ravg=60kpc and becomes strongly radially anisotropic, and that the velocity dispersion profile is consistent with the X-ray circular velocity curve at these radii without non-thermal pressure effects.