Euphoria from oxygen deprivation
Short answer
Given the fact that literature on hypoxia consistently report euphoria as a symptom, my conclusion is that the two are correlated strongly and is not confined to a small subset of susceptible people.
Background
Personally I know only of the effects of oxygen on the central nervous system under conditions of increased oxygen pressure, as for example encountered by scuba divers at depths greater than standard recreational diving. In that case it is called oxygen intoxication or oxygen toxicity (e.g., Chawla &amp; Lavania, 2001), characterized by e.g.:

visual changes
tinnitus
irritability, anxiety, confusion
vertigo.

Hypoxia (Asmaro, Mayall &amp; Ferguson, 2013) can indeed lead to

Euphoria and feelings of well-being
Acute anxiety, irritability &amp; confusion
confusion, loss of consciousness.

The authors however only qualitatively analyzed their group of test subjects on these subjective mind states and describe quantitative statistics only on psychophysical tests. The latter were indeed significant, showing that hypoxia leads to changes in performance on a variety of tasks in most, and probably all subjects.
To proceed to your question - hard numbers on the prevalence of feelings of euphoria are difficult to find, yet credible reports that mention it as a symptom are abundant. For example, the self-asphyxial risk-taking behavior (SARTB) you mention is known to lead to euphoria and is thought to be one of the motivations behind the 'game' (Griffiths, 2015; Busse et al., 2015).
The fact that hypoxia is a general term for a range of blood oxygenation levels, and the complexity of the cerebral cortex, variability in susceptibility is to be expected. For example, hyperoxic effects depend strongly on the altitude (i.e., partial oxygen pressure) Chawla &amp; Lavania, 2001).
References
- Asmaro, Mayall &amp; Ferguson, 2013
- Busse et al., Arch Dis Child (2015); 100(12): 1106–14
- Chawla &amp; Lavania, Med J Armed Forces India (2001); 57(2): 131–3
- Griffiths, Education and Health (2015); 33(3): 54-6