In the 19th century when steamboats regularly churned back and forth between NYC and Albany, they generally carried or transported both passengers and goods. Just like how trains don't stop at one station before making a return trip, steamboats often made multiple stops for passengers to efficiently reach different destinations. These also weren't typically just passenger ferries (with the exception of those involved in the tourism industry), but also functional towboats that dragged barges of goods up and down river. The practice of carrying both passengers and freight was very common and often what kept steamboat companies afloat so as to offset operating costs against seasonal changes in passenger traffic or strategically-lowered rates.

Besides its advantageous geography as a convenient halfway point on the river, Newburgh was also a major factory town with railroad connections, housing a station on the Erie and offering cross-river transport to Beacon and the NY-New England RR. Newburgh factories also produced a wide variety of goods and materials including fabrics and linens, soap, tools, boilers, furniture, candles, and so on. Many of these goods would have been in high demand both in an everexpanding NYC and the emerging towns along the Erie Canal. Finally, as was typical in many river transport networks, steamboat companies often had financial ties to certain cities and those cities' other industries. I haven't studied the Hudson that well, but it wouldn't surprise me if the owners of say, the Newburgh and Albany Day Line, had financial ties to other factories in both cities and other stops along the river such as Poughkeepsie.

All of this is to say that steamboats struggled to maintain pace against faster, more reliable railroads and frequently doubled as both passenger and freight transports to mitigate costs and remain competitive (again this doesn't necessarily include luxury vessels made for cruising/vacationing in the tourist hot bed that was the Hudson Valley). The implications of freighting, in conjunction with providing passengers access to multiple destinations, necessitated multiple stops, particularly at bustling factory/transit centers like Newburgh.

You can read more about Hudson River steamboating in Donald C. Ringwald's Hudson River Day Line: The Story of a great American steamboat company, (1990), but Newburgh isn't as discussed as other destinations.

Edit: I forgot to mention that it was not entirely unusual for companies like the Day Line to have boats dedicated specifically to express and multi-landing trips. The Day Line started doing this in 1876 in anticipation of the Centennial Exhibition in Philadelphia. (Ringwald, Hudson River Day Line, 51).