[He believes that he's important to her and, right now, he feels like her kiss is saying that she could love him someday. The hope of that is enough for him.
There's a Russian saying (just ask him) that goes something like this: "Hope for the best, prepare for the worst." Maybe it's a bleak way to live, but it's an approach that has served Chekov well so far. Ultimately, he is a realist. He understands that not everyone rushes into love as quickly and eagerly as he does, and even fewer people find themselves rushing towards someone who will return their love. Even in situations that don't involve multiple universes and other extenuating circumstances, people often need to be content with a reality that is less than ideal. There are always conditions. There will always be difficulties and snags and hurdles, and the only way to be happy with most outcomes is to hope for the best while accepting that the end result will fall short of expectations.
He has fears, of course. He's afraid of losing Kitty or being pushed away. He's afraid that he'll leave, which is something that he has done several times (albeit in very different contexts), and he's afraid of being hurt. Some part of him is perpetually prepared to deal with worst-case scenarios and fears coming true.
But he also hopes for the best and, for him, hope wins out over fear. As long as he has something to hope for, he can be happy.
He's happy with whatever affection and devotion Kitty is ready to give. Chekov doesn't need to guard himself or hold back because, even though he knows he can withstand the worst, he has hope for the best.
While three extra years have made Chekov more firm in this worldview of his, he's still thrown off and rattled and slightly disoriented. He needs time to catch up with himself before he gets more carried away than he is, but maybe that hope and happiness come across regardless. He's certainly not trying to get out of kissing Kitty.]