Interesting question from the OP. I've wondered this myself - here are a few thoughts and observations.
First, regarding a definition, I would say that someone who has an interest in audio gear beyond the music they play through it could be called an audiophile. If they thoughtfully assembled their system and could tell you the brand names of their components that's enough for me.
Regarding numbers, it's harder. There are about 70K Stereophile subscribers and about half that for TAS. I suspect that many of them, like me, subscribe to both publications. Anyone who reads these publications can certainly be called an audiophile. I suspect that the number of people who feed their hobby with the internet is larger. Michael Fremer has put out videos that have totaled several hundred thousand views. I would call anyone who watches a Michael Fremer video an audiophile. When you estimate how many people subscribe to online reviewers or participate in forums the number is surely in the six figures but there is a lot of overlap with other media.
So, I would estimate that the number of audiophiles is probably somewhere south of 500,000 world wide with maybe 300,000 of them in the US. This number makes sense to me because it would take a market like this to support the industry that we have.
Is the population of audiophiles growing or shrinking? The evidence is clear to me that our numbers are growing. One only has to look at the increasing number of manufacturers and the explosion of products to determine that this is a healthy market. New models are constantly being introduced at every price point and new types of gear is filling out the product offerings. The amount of gear available is staggering and it is only getting bigger. New audio shows are popping up across the country. I attended the first Pacific Audio Fest (Seattle) last summer and it was a huge hit. New retail stores are opening up. Yes, some have closed, but more new ones are coming on the scene and expanding the retail presence. Everything I see points to an expanding market and a growing base of people who I would call hobbyists or enthusiasts (i.e. audiophiles).
I'm 67 and I worked in senior management most of my career. I have only met one other audiophile in all that time outside of an audio show. One way to put this in perspective is to compare how many LGBTQ people I have met vs. audiophiles. Gallup estimates that 7.2% of the US population is LGBTQ. I couldn't begin to tell you how many queer people I have met or known throughout my life but it is a lot. But only one audiophile. Maybe we don't come out of the closet except at audio shows.