Does the Same Principle of Non-Optimality Apply to an American Call Option That Is Only Slightly In-the-Money?

Yes, the principle of non-optimality for early exercise still applies to a slightly in-the-money American call option on a non-dividend-paying asset. The option still has time value, and exercising early would forfeit that value.

Selling the option is always the financially superior choice, as the market price includes the intrinsic value and the time value.