Sure enough I disassembled my other road bike cassette (also Shimano) this morning, and cogs have no play whatsoever between them.
Which means that my cassette evidently took some battering (?) and some of the cogs holes thru which the rivets go have enlarged somehow.
Even though it works, on the bike, it is not as supposed to be and I will replace it since it is not expensive. However, a five months cassette shouldn't be in these conditions (if it was better quality).