Here's how a person would NOT be a "beta" in that situation
First: Don't freak out over sharing an ice cream cone, or a drink, or a bite of food or whatever bullshit you think is an "indirect kiss". The whole concept of an indirect kiss is dumb as shit prudishness.
Second: When a girl starts kissing and licking on your neck... A) If you're not interested, gently remove her and tell her firmly, "I'm sorry, but I don't have feelings toward you that way" or B) wrap your goddamn arms around her and start kissing her back.
You can do A or B and not be a beta.
This MC, however, appeared to just stand there in shock for as long as it took for her to slurp up all the ice cream from his neck, for his ice cream cone to melt, and then for her to start sucking on his fingers - this must be a good 20-30 seconds at a minimum where he just stands there completely shell-shocked, doing nothing. This is BETA behavior.
It's not as bad as like, freaking out and screaming and flinging yourself away from her with a nosebleed while apologizing and making excuses and throwing yourself into a dogeza (personally that kind of behavior is where it goes from "beta" to "beta-cuck", because at that point you're actively attempting to prevent yourself from advancing romantically -- see the Rental Girlfriend manga for examples).
An MC doesn't have to start fucking every girl in sight immediately to be alpha. All he has to do is be confident in who he is, even when he's around girls who are interested in him , and around girls that he is interested in himself.
So how could someone respond in a non-beta way? Here's just an example:
A girl suddenly grabs onto your arm and you feel her boobs pressing into you? Instead of starting to sweat while freaking out about something 'soft' touching him, how about an MC instead be like, "Wow, just couldn't wait to grab hold of me, could you? I'll make sure to return the favor later." or "Whoa! Good morning to you too, cutie. You sure smell nice today." or "Hey, I know I'm popular, but no jumping the line just because you're pretty! Oh well, I guess I'll make an exception for you today."
Or like, if the MC is out around town with a girl he likes, but it's early and there's been no romantic development yet and some idiot is like "Whoa, a boy and a girl together, this is OBVIOUSLY a date! (because, you know, no one could just be friends or whatever in Japan).. instead of stammering, "D-d-date!?!? N-no, we don't have any kind of relationship like that!", a real man would turn to the girl and say, "Well we were just hanging out, but how about we make it a date from here on out?", or to the person being an idiot and interfering, "Lucky me, right? I get to take a girl this pretty out on a date! Ah! So that's why you're sticking your nose in someone else's business -- you must be jealous!" (and then take her hand and walk away).
Anyway, there's all kinds of ways not to be a pussy, and for some reason there's lots of non-pussy guys when it comes to like, killing a dragon or taking down a mob boss, but very few MCs who can hold a girl's hand with the same kind of bravery, and it's really fucking sad.