Thanks Udo for your response.
On my PC that previously was on W8.1 the startup time is also ~7 s. CDF Player 10.2.
On the other PC, previously W7, I have given up. After much experimenting. Now rolled back the machine to its W7 origin. And CDF Player starts, as before, fast.
Besides the difference in original OS between the two PC's there is another difference: The "good" PC has both Mathematica and CDF Player installed. The "bad" PC has CDF Player only, not Mathematica.
Question: On your PC, do you have both Mathematica and CDF Player installed? Or the CDF Player only?