Working in Yafiz, Sha'ar Binyamin, I can attest to the fact that that local Arab Muslims buy presents to celebrate all sorts of Moslem holidays. The Rami Levi commercial empire certainly benefits from that custom. Moslem holidays "travel around" the calendar, because it's a totally lunar calendar without solar adjustments. The Jewish Calendar combines solar and lunar, so holidays will always fall in the right season.
Chanukah and Christmas coincide, give or take a few days or a week or so. In an early pre-leap month Jewish year, Chanukah will end a week or so before Christmas, but in most years Christmas will fall in Chanukah. Please don't forget that Judaism predates Christianity and both predate Islam. I think that fact is a very important one to remember. Of those three major religions, Judaism is the most veteran, the oldest. The other two, Christianity and Islam, base much of their histories and territorial claims on Judaism in a double-punch attempt to replace Judaism, aka identity theft.
All Jewish Holidays revolve around food and eating. There are lots of jokes giving that as the punch-line.
Would Chanukah presents for the kids, spouse and more be the custom if the holiday didn't coincide with xmas shopping season?
There's an awful irony if the answer to that question is "NO!"
Chanukah is the Jewish Holiday that celebrates the fight against assimilation to foreign, non-Jewish cultures. In the media and commercially dominant western Christian culture of today, this is shopping and gift-giving season. I don't see all that shopping as being connected to the Jewish Holiday of Chanukah. During Chanukah we're supposed to add the Al HaNissim, Because of The Miracles to all of the prayers we say during the eight day holiday. It explains what we're celebrating and why:
תפילת "ועל הניסים" לחנוכה
על הניסים ועל הפרקן ועל הגבורות ועל התשועות ועל המלחמות שעשית לאבותינו בימים ההם בזמן הזה:
בימי מתתיהו בן יוחנן כהן גדול, חשמונאי ובניו, כשעמדה מלכות יון הרשעה, על עמך ישראל, להשכיחם תורתך ולהעבירם מחקי רצונך, ואתה ברחמך הרבים, עמדת להם בעת צרתם. רבת את ריבם, דנת את דינם, נקמת את ניקמתם, מסרת גיבורים ביד חלשים, ורבים ביד מעטים, וטמאים ביד טהורים, ורשעים ביד צדיקים, וזדים ביד עוסקי תורתך, ולך עשית שם גדול וקדוש בעולמך, ולעמך ישראל עשית תשועה גדולה ופרקן כהיום הזה. ואחר כך באו בניך לדביר ביתך, ופנו את היכלך, וטהרו את מקדשך, והדליקו נרות בחצרות קדשך. וקבעו שמונת ימי חנוכה אלו, להודות ולהלל לשמך הגדול
And [we thank You] for the miracles, for the redemption, for the mighty deeds, for the saving acts, and for the wonders which You have wrought for our ancestors in those days, at this time—
In the days of Matityahu, the son of Yochanan the High Priest, the Hasmonean and his sons, when the wicked Hellenic government rose up against Your people Israel to make them forget Your Torah and violate the decrees of Your will. But You, in Your abounding mercies, stood by them in the time of their distress. You waged their battles, defended their rights, and avenged the wrong done to them. You delivered the mighty into the hands of the weak, the many into the hands of the few, the impure into the hands of the pure, the wicked into the hands of the righteous, and the wanton sinners into the hands of those who occupy themselves with Your Torah. You made a great and holy name for Yourself in Your world, and effected a great deliverance and redemption for Your people Israel to this very day. Then Your children entered the shrine of Your House, cleansed Your Temple, purified Your Sanctuary, kindled lights in Your holy courtyards, and instituted these eight days of Chanukah to give thanks and praise to Your great Name.
That's what the Chanukah holiday is all about.
PS Just in case you're curious, I will give small gifts to the kids when we get together. But I hope and pray that it's the being together that will be the biggest gift of all, the great celebration, not the trinkets.