Oh dear heavens, that dictionary is awful! For an English-Phoenician dictionary, you'd be much better off using Richard S. Tomback's A Comparative Semitic Lexicon of the Phoenician and Punic Languages (Missoula: Scholars Press, 1978) or--more problematically--Charles R. Krahmalkov's Phoenician-Punic Dictionary (Leuven: Peeters, 2000). Eventually, I hope to upload an up-to-date online dictionary (it's only about 20% done right now).

As far as I know, no word for "alphabet" is attested in the extant corpus of Phoenician-Punic texts. One Punic inscription does contain the curious note wktbt msprm ’rb‘m wšlš, which Krahmalkov translates: "As for the letters <in the preceding portion of this inscription>, their number is forty-three." He takes ktbt as a noun meaning "letters" (cf. Biblical Hebrew כְּתֹבֶת), as in the letters of the alphabet. However, ktbt is more likely to be a verb, and the section should thus be read: "...and I have written the number (of characters), forty-three."

Since the Phoenicians seem to have called themselves "Canaanites" (kn‘nm), I would speculate that they simply referred to their language (alphabet and all) as the "language of Canaan" (špt kn‘n, as it appears in Hebrew in Isaiah 19:18). Krahmalkov briefly acknowledges this but doesn't go anywhere with it.