In the video, a 300 litre receiver is mentioned (around 80 Gallon).
80mm bore x 200 stroke is as near as dammit one litre. In round figures, there are 30 litres to a Cubic Foot.
If we feed at 100 PSI(g), we'll need about 7.5 litres of free air per working stroke, or 1/4 Cubic Foot.
It'll need a little less for the return stroke. How much less will depend on the diameter of the rod and this is not given. Worst case would be an infinitely thin rod and the same air volume again for the return stroke: half a Cubic Foot per full stroke cycle.
Blows-per-minute is obviously the big variable. On a small power hammer, full speed is likely to be 200 bpm or a little more. That would suggest 100 CFM as potential air usage.
My guess is that the power hammer is only ever going to be run in short enough bursts that the compressor size is largely irrelevant and the receiver capacity alone determines how much air you are going to get.
Size-wise, it seems broadly comparable to the BigBlu 65 Max. That seems to have a 2.5" x 7.5" cylinder (the website says "2" (63.5 mm) bore cylinder with double wear bands." and "7.5" Adjustable Stroke" Since 2" is 50.8mm and 2.5" is 63.5mm, it seems likely the 2" is an error and should read 2 1/2"). The BigBlu claims a maximum of 220 bpm, "runs effectively at 90 psi" and "Average air consumption during hot forging is 14-16CFM-Normally paired with a 3.5HP to 5HP compressor with an 80 gallon tank".
14-16 CFM at 90 PSI is around 98-112 CFM FAD, so, assuming the BigBlu numbers are realistic, it looks like things are probably in the right ballpark.
It is worth noting that an 80 x 200mm cylinder has 66% greater displacement than a 2.5" x 7.5" cylinder, so it's probably fair to say a compressor of 5hp or more would be appropriate for the unit in the video. Bigger, as noted, would be better.
Another way of looking at things is that, if the 300l receiver is initially charged to 10 bar(g) (150 PSI) and the supply to the hammer is regulated to 6 bar(g) (90 PSI), there will be 1200 bar litres of free air available without running the compressor. At 15 litres/cycle, that would give around 80 blows before pressure to the hammer starts to drop.
It is worth noting that 2-stage compressors seem to be much less common in Europe than in the US and that 6 bar is usually considered "normal" supply pressure over here. With a 2-stage compressor charging to 200 PSI (13.5 bar), a 300l receiver would provide 1950 bar-litres of available free air and allow 130 blows.
