You could use perl (not a perl guru by any stretch, so may be more complex than necessary)
perl -n -e 'BEGIN {$cnt=0} END { print $cnt."\n"} /dateTime="\d{4}-\d{2}-\d{2} (\d{2}:\d{2}:\d{2})/ && $1 ge "08:00:00" && $1 lt "10:00:00" && $cnt++' < log.txt
...or for readability;
perl -n -- runs the script for each line in the input file
BEGIN { $cnt=0 } -- start by setting $cnt to 0
END { print $cnt."\n"} -- when all is done, print $cnt
/dateTime="\d{4}-\d{2}-\d{2} (\d{2}:\d{2}:\d{2})/
-- match for time format, keeping the time in the group
$1 ge "08:00:00" -- check if the time is greater or equal to 08:00:00
$1 lt "10:30:00" -- check if time is less than 10:30:00
$cnt++ -- if all matches are ok, increase cnt
EDIT from the comments;
/dateTime="\d{4}-\d{2}-\d{2} (\d{2}:\d{2}:\d{2})/
...basically is a regex that matches the rows with the datetime field format you're giving (4 digits + - + 2 digits + - + ...) and extracts the time part (the parenthesized part) into $1 for comparison with the limits. It should work for any time span within a single day, so 10:25-10:35 should work just fine.
