UPDATE: this information is now obsolete, see first reply to this post.
M'ath eyak!
To improve my understanding of the Dothrai language and better my Bible translation I've gone back to all the dialog available and found some interesting tidbits I thought I'd share concerning expressing purpose in Dothraki.
Expressing purpose in Dothraki was my weakest area in Dothraki grammar and was the main reason I went back to the dialog. You can express the purpose in Dothraki in a couple of ways:
The verb movekkhat[to be intended for, be for] is clearly meant for expressing purpose:
Mas ovray movekkhi moskay.
The remaining valuables are for loading. Jorah S2E10
There is, however, something fishy about this construction. This is the only instance of a concatenative verb taking the present participle rather than the infinitive form of a verb. The fact that Jorah, a non-native speaker, is the only one heard using it and that the gerund/present participle is also used in the English translation make me wonder if this is not a non-native speaker's mistake, and the sentence should in fact be *mas ovray movekkhi moskat. Both Spanish and English have concatenative verb +infinitive and concatenative verb + gerund/present participle constructions, though, so perhaps not.
If you want to say something is good for some purpose, you might also use the verb davralat:
Haesh rakhi davrae zafraan.
Lamb men make good slaves., or, Lamb men are good for slaves. Rakharo S1E8
Let's say you want to express the purpose of a noun in a clause; a simple relative clause of purpose will do the job:
Ador finaan khal nevasoe.
A chair for a king to sit on. (lit. A chair that a king sits on.) Dany S1E7
Again, here's Khal Drogo, dropping the relative pronoun but otherwise expressing the same idea:
Khal vos zigereo adoroon anevasoe maan.
A khal doesn't need a chair to sit on, or A khal doesn’t need a chair [he] sits on it. Drogo S1E7
If you've studied Latin, you know that purpose and result can be muddied together and treated the same way. Dothraki seems do something similar, using majin plus a verb in the future tense to tie together the main clause and subordinate clause:
Khal Drogo vazhoe mora azzafrokea, majin azzafroki vazhi kishaan ma hoshor ma tasokh ma tawakof.
Khal Drogo will make a gift of them to the slavers, and/and so/so that the slavers will give us gold and silk and steel. Rakharo S1E8
You might even drop the majin, as one of Khal Moro's wives does here:
Khal Moro: Hash khal drivoe, hash at gachi disse vekha ha khaleesisaan mae.
Wife #1: Vaes Dothrak. Vaesof Doshi Khaleen.
Wife #2: [majin] Athira asshekhis mae ma khaleenisoa khali drivi.
Khal Moro: When a khal dies, there is only place for his khaleesi.
Wife #1: Vaes Dothrak. The Temple of the Dosh Khaleen.
Wife #2: To live out her days with the widows of dead khals. Or, [and so] she will live out her days with the widows of dead khals S6E1
And earlier from Qhono:
Anha vo zigerok meme deva ahilek mae vi choyokh.
I don't need that she [is smart?] I will 'hit' her through the ass. Qhono S6E1
You can see both in action in the Dosh Khaleen Priestess's words in S6E3:
Ei khalasari ray essash vaesaan ershe haji Khalaroon Vezhvena, fini ashiloe mori ajerie ostirge mori haji aheshkoon sila meshes.
All the khalasars have returned to the ancient city for the Khalar Vezhven, who will meet[and so]they discuss their plans for the coming winter. Dosh Khaleen Priestess S6E3
Using verbs like movekkhat and davralat, relative clauses, and majin plus the future tense, Dothraki is able to comfortably express purpose.