May one give presents on Chanukah or is this Minhag Hagoyim due to Kratzmacht?[1]

Yes, one may, and so is the Minhag Yisrael to give out Chanukah Gelt on Chanukah. The reason is because Minhag Hagoyim only applies to customs that have no logic. Giving presents on a Holiday has logic and source in Torah, such as by the Shalosh Regalim when the Husband and father must buy gifts for his wife and children so they be happy during the festival.

[1] See regarding giving presents and monetary gifts on Chanukah: Toras Menachem 5748 2:65; Likkutei Sichos 20 p. 452; Rebbe in Shaar Halacha Uminhag 2:283; Shulchan Menachem 3 p. 288-289; Sefer Haminhagim P. 161; Emes Leyaakov 570 footnote 583; Avnei Yashpei 1:129-2; Sifsei Chaim Moadim 2:134; Orchos Rabbeinu 3:1-2; See regarding the prohibition of Darkei Emori and that it only applies against following the illogical customs of the Goyim: See Rama Y.D. 178:1 “This is only forbidden if the clothing of the gentiles are worn by them for sake of frivolity [pritzus] or it is a gentile custom that has no logic behind it, as in such a case there is room to suspect that the custom derives from the Emorite customs, and that it derive from practices of idolatry passed down from their forefathers.”; Maharik 88; See Kapos Temarim Yuma 831 and Chavos Yair 234 that Darkei Emori applies towards practices that the gentiles developed as a result of idolatry, that they believed that these actions invoke their G-ds to give assistance. See also Ran on Shabbos 67a; See Admur 301:33 “Any medical treatment that works in accordance to Segulah [i.e. supernatural causes] rather than natural cause and effect [i.e. scientifically based] does not contain the prohibition of Darkei Emori so long as it is recognizable [to the onlookers] that it’s intent is for the sake of healing”; See Igros Moshe E.H. 2:13; Y.D. 4:11-4; O.C. 5:11-4