We report the detection of extended warm ionized gas in two powerful high-redshift radio galaxies, NVSS J210626-314003 at z = 2.10 and TXS 2353-003 at z = 1.49, that does not appear to be associated with the radio jets. This is contrary to what would be expected from the alignment effect, a characteristic feature of distant, powerful radio galaxies at z ≥ 0.6. The gas also has smaller velocity gradients and line widths than most other high-z radio galaxies with similar data. Both galaxies are part of a systematic study of 50 high-redshift radio galaxies with SINFONI, and are the only two that are characterized by the presence of high surface-brightness gas not associated with the jet axis and by the absence of such gas aligned with the jet. Both galaxies are spatially resolved with ISAAC broadband imaging covering the rest-frame R band, and have extended wings that cannot be attributed to line contamination. We argue that the gas and stellar properties of these galaxies are more akin to gas-rich brightest cluster galaxies in cool-core clusters than the general population of high-redshift radio galaxies at z > ∼ 2. In support of this interpretation, one of our sources, TXS 2353-003, for which we have Hα narrowband imaging, is associated with an overdensity of candidate Hα emitters by a factor of ∼8 relative to the field at z = 1.5. We discuss possible scenarios of the evolutionary state of these galaxies and the nature of their emission line gas within the context of cyclical AGN feedback.