Should we create a new tag for these riddles? What would we call it?
I don't think we need a new tag, for the same reasons I give in the “prefix-suffix-infix” riddles meta question (I believe this is an identical situation).
Again, this is just one specific construction of a riddle using one specific example of wordplay. There are plenty of other examples of riddles that use the technique of adding/dropping letters, describing the results as it transforms (1, 2, 3, 4, 5, 6, 7, 8, ...).