Yes, not every kid has the capacity for physical demonstrativeness, but that doesn't necessarily indicate a lack of love. One of my sons only likes physical affection if he initiates (rarely), and it has to be on his own terms. I couldn't just go up to him and put my arms around him, to him that would feel uncomfortable or even hostile. This has been hard at times, such as when he has been hurt or upset and it is my instinct to want to comfort him with a hug and I have to fight against that. But he shows and accepts love in different ways. Just last night he said, "Mom, I appreciate you." (I have an injured foot and haven't been able to take care of my usual duties. Apparently he is noticing how much I usually do in the absence of having it done!)
Also, a little off topic, but being physically affectionate with my kids didn't come naturally to me as a parent. I have never been particularly touchy-feely, and dislike unexpected touch, but when my sons were very little their sensory needs were different than now, and they were constantly all over me (hugs, kisses, sitting on my lap, just standing against me or touching me often). So I had to go through the process of learning to be "touchy" for them, and then learning to back right off as their sensory profiles changed and they became defensive instead of seeking.
Either way, none of it is about love. It's about sensory needs and preferences.