The new Keynesian IS curve: What determines output? The New Keynesian IS curve can be described by the following (log-linearisation around the steady-state):$$y_t=E_t(y_{t+1})- \frac{1}{\theta}(i_t - E_t\pi_{t+1}-\rho)$$
where $\displaystyle\frac{1}{\theta}$ is the intertemporal elasticity of substitution in consumption, $\rho$ the discount rate,  and the remaining terms have their usual interpretation.
In the book Dynamic Macroeconomics, by Alogoskoufis, in chapter 16 (page 461), the author states:

Recall that this is nothing more than the Euler equation for
consumption, supplemented by the assumption that all output is
consumed, and the same relation was derived in the new classical model [it's eq. 14.10]
of chapter14. However, in contrast to the new classical model, where
output is determined by aggregate supply, in this model, because of
staggered pricing, output is determined by aggregate demand. Thus, it
is the IS curve that drives output ﬂuctuations.

I do not understand in what way is the output being determined by aggregate supply in the free price setting, nor by the aggregate demand in the sticky prices one.
The solution to your question is price stickiness, or as the author calls it staggered pricing. Let's assume a typical question in the Basic New Kenesian DSGE Model: What happens when a technological shock hits the economy?
More productive firms can produce cheaper but may not be able
to lower their prices due to price rigidities thus demand from the households stays at a lower level. The market clearing condition is supply equals demand and since demand won't increase output in the economy will be constraint (your paper uses determined but this might be the source of confusion) by the demand side. In this scenario one speaks from a negative output gap (Output is depressed in comparison to a world with flexible prices). In a flexible price scenario firms can lower their prices and thus household simultaneously increase demand, as firms want to increase production.
If you want to know more about price stickiness the basic DSGE models often implement the form suggested by: Calvo, Guillermo, “Staggered prices in a utility-maximizing framework,” Journal
of Monetary Economics, 1983, 12 (3), 383–398.