Alignment is not restricted to "gapped" alignments only (or there wouldn't be a need for such a distinction!).
You can modify the algorithm to include gapped alignments (by introducing gaps in your search sequence), as it supports a "gap" character ("-"). The gap character will just always count as "not a match."
[1] http://en.wikipedia.org/wiki/Boyer%E2%80%93Moore_string_sear...
I am not sure you understand what gapped alignment is- it is not the alignment of a sequence with known gaps, but an algorithm which determines the best placement of gaps in a query sequence to obtain the highest matching score. This is a very different problem than the one you just described, and is essentially "the hard part" of sequence alignment. [1] http://en.m.wikipedia.org/wiki/Sequence_alignment
Turns out they aren't actually after an alignment per se, but rather trying to match a DNA binding motif.
(You're right though about this not being an alignment, rather just a substring search with degeneracy).
"In bioinformatics, a sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships between the sequences." (From the article you linked.)
Gapped sequence alignment is certainly far more robust (and biologically relevant - insertions are a common error - when comparing sequences across organisms) than ungapped, and a much harder problem, but as for the definition of "alignment" itself, I don't believe I've misnamed anything here.
If we're going to be overly pedantic about the use of the word "alignment" that's fine, but I'm not sure it's a worthwhile debate to have. A quick search for "ungapped sequenced alignment" returns a great deal of results on Google [1]. So if I am mistaken, I'm certainly not the first (nor do I believe I'll be the last.)
Furthermore, there's nothing preventing anybody from using the methods described here from implementing an ungapped sequence alignment tool that outperforms tools that only use string comparisons. :)
[1] https://www.google.com/search?q=ungapped%20sequence%20alignm....
tools like BLAST are extremely sophisticated and have been under development for decades, and I'm fairly confident they've moved past naive string comparisons by now.
And to be clear, nowhere am I comparing what I've developed to BLAST. (They have very different applications.)
[1] http://schneider.ncifcrf.gov/paper/malign/