Some of this yes. Some of this no.
Every arm and leg wiggle, every eye blink, every coo and fart and startle.
This is the no. First of all, at this phase the child is a synesthete. The arm and leg wiggles are not communication but stimulus response. Espying the color red may be why the leg wiggled. While delightful to a parent, don't make more of it than it is.
Also, they cannot coo at this stage. You may have confused the social smiling/cooing phase for what the OP is commenting on. The OP is referring to far earlier in development.
The startles are reflexive. The Morrow reflex. It is also not communication. It is just an instinct hardwired in to a primate brain to prevent newborn death by putting the primate newborn in a position to grab on to an adult's body fur and thus prevent falling to their death.
I find this phase personally delightful because you get to see the human BIOS on which their person operating system is shortly to be installed, but it is absolutely okay for people not to, just like some computer enthusiasts love a BIOS and others don't. So long as one isn't neglectful, it is okay to not be enthralled.
I like to play a game I call toddler fetch. You throw a ball, and then they go fetch it and bring it back to you, and then you throw it again. You can use a soft inside ball to do that.
Another game I like to play involves them running back and forth across your field of vision, and you have a ball, and your goal is to hit them as they run back-and-forth. This is usually a soft ball, and an indoor activity, and you need to be intentionally bad at hitting them because the whole point is to get them to run back-and-forth and get tired. I play this particular game while sitting down, when I'm tired myself.
As a non-verbal crawler, they can still do a version of toddler fetch which is more like crawler fetch. Since they are crawling they will have to dribble - think soccer - the ball back to you instead of simply bringing it as would happen in toddler fetch. While you can explain the rules, it does help to just simply get excited when they bring the ball back and they figure that out really fast.