Batteries can usually withstand peak currents that are well above the 1 hour rate.
In your example, dividing the Wh rating by the voltage gives the Ah (Amp hour) rating of 4.4 Ah, which means that if you take 4.4 A, it would be discharged in 1 hour.
That does not mean that 4.4 A is the maximum current. The maximum current allowed isn't clear from the Ah rating. It depends on a lot of things, but heating is one of the factors. The battery might well overheat if you took a high current from it for a long time, but the laptop could well take peaks of 10 A or without problems. As long as the current peaks are short enough that the battery doesn't have time to overheat, that would be fine.
The 1 hour rate is a very crude guide, and I would say that it is usually for continuous use, and there are lots of applications that discharge a battery far faster than 1 hour. Drones and cordless power tools are two examples of common devices that don't last anywhere near 1 hour if used continually. On the other hand, some battery chemistries, especially on non-rechargeable batteries, are not suited to short discharge times. Lithium Thionyl Chloride batteries are an example, as they have a huge capacity but can't be discharged efficiently in less than about 100 hours.
As for peak current, many applications have peak discharge rates that are far more than the 1 hour rate. 2G mobile phones take large current peaks, as do vehicle starter batteries. Electric vehicle maximum power ratings are often around 3 - 4 times the kWh rating of the battery.