The verb "يقدر" "Yuqadd-deru" = roughly means"to estimate / evaluate" (root: قدر).
"قدره" = the word "قدر" "Qadr" = "estimate or value" (Noun of previous verb) with the enclitic pronoun "ه" = "his value".
The word "حق" "Haqq-qa" = "reality / truth" (root: حقق).
The expression :"يقدر (الشئ ) حق قدره" = "to evaluate / estimate (something) to its true value"
Since the sentence is negative, "لا يقدر (الشئ) حق قدره" = he does't estimate (something) to its true value / degree" , in other words "he underestimates it".
Full translation would be something like:
فقلت في نفسي: إنه لا يقدر ما نحن فيه من الخطر حقَّ قدره وكيف له أن يدرك وهو لا يجوع ولا يعطش
"I said to myself: He underestimates the danger we are in, and how would he understand ( / realize) , since he neither goes hungry nor thirsts".
(in other words, because he doesn't feel hunger or thirst, he underestimates the danger they are in)