Hi Norse, that sounds like exactly what is happening. It is natural when two people develop and deepen their relationship. It doesn't always happen, but it's normal. My mother and father met online many years ago. She was in US and was in Australia, which is something like 13,000 miles away. They both described similar things between them as they grew closer in their bond and relationship. :) Enjoy it, it can be a lot of fun, and give you both some great and even funny memories. Sometimes it can even save a life. There are even exercises the two of you can do to strengthen the connection.
Good luck to the both of you!