What part of speech is the word "smiling" in this example?

The present participial (participle) is formed from the verb stem normally by adding -ing to the infinitive with some variation based on the final letters of the stem. Thus to smile becomes smiling. The participle can act as a nonfinite verb, adjective, noun, or as part of an adverb clause. [The Chicago Manual of Style]

Some examples:

Smiling is good for you. - Noun [Gerund]

I love to see your smiling face. - Adjective

Joe ran from Melissa, smiling as he went. - Nonfinite verb [Joe was smiling]

She was grinning, smiling even, as she walked up to the podium. - Participle phrase being used as an adverb

But what about:

I said, "Look at those two smiling over there!"?

I see "smiling" differently in your examples:

1. Smiling is good for you: verb interpretation preferred (cf. "To smile is good for you"), but noun interpretation can be forced by adjectival premodification, as in "occasional smiling")

2. I love to see your smiling face: verb pre-modifying the noun “face”.

3. Joe ran from Melissa, smiling as he went: verb heading the clause "Smiling as he went" as predicative adjunct with "Joe" as predicand.

4. She was grinning, smiling even as she went …: verb (coordinated), part of present progressive aspect.

And your question: Look at those two smiling over there: verb as head of subordinate clause "smiling over there", modifying the NP "two".

Breaking it apart will be helpful here.

First, there's an implied subject in this imperative construction: "[You] Look at those two smiling over there"

1. [You] = subject
2. Look = verb
3. At those two smiling over there = prepositional phrase, functioning as a adverb modifying "look."

Going further with our object,

3.1. At those two smiling = prepositional phrase

3.2. over there = prepositional phrase, function as an adj modifying "those two"

Within 3.1, we also see that "those two smiling" is the object of the preposition "at."

Thus, "smiling" modifies the noun phrase "those two," and should be taken as an adjective.

It's important to keep the grammatical relations (or syntactic functions) separate from the parts of speech.

1. Smiling is good for you.
2. I love to see your smiling face
3. Joe ran from Melissa, smiling as he went.
4. She was grinning, smiling even, as she walked up to the podium.
5. Look at those two smiling over there!

The probable reading is that smiling is a gerund-participle verb in each example in 1-5 above. However, the grammatical relations in each sentence are different. In those sentences where the grammatical relations are those we associate with nouns, traditional grammar would call them gerunds. In all other instances, where they head clauses functioning as Modifiers of some description, traditional grammar calls them participles. In many modern grammars they are just recognised as the -ing forms of verbs which can do different jobs in a sentence or phrase. We call these gerund-participles. They head gerund-participle clauses. I'll call these clauses GP's for short

In (1) the GP is Subject of the sentence. In (2) the GP is the modifier of a noun (the same kind of job that adjectives and nouns can both do as well). In (3) it is an Adjunct, more specifically a Predicative Adjunct describing the Subject, Joe. In (4) the GP is part of a co-ordination (it means something similar to the coordination in she was [grinning and smiling]) which is functioning as Complement of the verb BE. In (5) the GP is post-modifying the word two, in the same way that an adjective phrase or relative clause might.

Remember that even though many of these functions (Subject, Modifier and so on) are functions that may be done by noun phrases or adjectives, this does not make the verbs doing these jobs nouns or adjectives. They are verbs! Specifically, they are gerund-participle forms of the verb.