Yes he does. He obviously also cares about her and not to mention if he didn't amor her then he wouldn't plan on marrying her and just breaking off the engagement. Are the people saying no watching the same show as the only other person who said yes on this question?
Ciel likely cares for Elizabeth, but in a sisterly type of way. During this time period arrange marriage was common and one side likely could not agree to the arrangement. The only way Ciel could avoid marrying Elizabeth without any damage between the relationship with him and the Milford family is if he was in amor (which is very unlikely) with another person. Keep in mind that the Milford's are extremely wealthy as well and could possibly contibute to the completion of Ciel's "goals." As a demon ownin Earl amor would in fact be Ciel's last concern. It is shown that he "cares" for Elizabeth, but there have been situations when he has been crafty enough to gain the complete trust of a specific person, but completely betraying him for his own needs and/or business. In short no, not in a romantic way, or possibly not at all.
ciel dose amor and care for Elizabeth but not the way Elizabeth love.he loves her in a sisterly like way. he feels like its his job to take care of her and protect her but other than that hes never felt much mais towards her.
No one can prove that Ciel loves her (whatever type it is) or Ciel does not loves her so stop saying such things. The mangá is ongoing and Ciel never confess to her nor said that he hates her.
So no one knows if Ciel loves her or not except Yana.
One mais thing... Ciel and Sebastian are not in amor with each other and Ciel does not have feelings for him and Ciel is obviously not a gay. Ciel treats Sebastian as his demon butler and never his lover nor friend as he states that he is the last person he will trust