Long and short vowels were written the same way in Old English (macrons, the lines marking long vowels, are a modern convention). Given the current pronunciation of Christ, I’d guess it had a long and not a short vowel in Old English. But I’m not sure. If it did have a long vowel, the reason might be because Latin Chrīstus apparently had a long vowel.
The Ormulum (early Middle English) uses the spelling Crist (where the non-doubled s indicates a long i) alongside Crisstene and Crisstenndom.
If the word really did have a short vowel in Old English, French influence could possibly be a reason for the pronunciation with a long vowel in Middle English. Monosyllabic words ending in /st/ taken from French, like coast, toast, feast, fairly often have long vowels for some reason.
I looked at the Oxford English Dictionary entry for Christ, and it says the length of the vowel in Old English is "uncertain".
It isn't a case of homorganic lengthening of the type found in child: that lengthening process was an early sound change that only regularly applied before consonant clusters ending in a voiced consonant, not ones like /st/ ending in a voiceless consonant.