Sweating is one the main triggers for an increase in blood plasma volume, and the humidity level of a steam room causes vastly higher rates of sweating than most saunas do. You can lose significant body heat by sweating in a dry environment, but much less in high humidity. Consequently, your body needs to sweat much more rapidly even though the absolute temperature may be lower.

To my understanding, while sweating is important to heat adaptation and blood plasma volume adaptations, thermal load and cardiovascular strain are likely bigger factors (and more important for the health benefits mentioned in this study). Overall thermal load is still higher in a hotter dry sauna than in a steam room