I mean really, the rules are the rules, and there is no ambiguity. So a "strict reading of the rules" is the same thing as a "reading of the rules." Because, as you say, there is no such thing as a reading of the rules that violates the rules and is thus merely "less strict."

For example, under the rules, not moving a piece you touched and promoting to the other color are the same: illegal.

The examples you are giving are simply cases where the other player is likely to let you break the rules if it's a very casual game.

So again, having "strictly" in the sentence is, technically, purely redundant.

It's a dumb thing to say, but then again, it probably made the piece more suspenseful and thus more fun to read.