In this chapter, Moses reminds the Israelites of their obligation to offer their first fruits in the Feast of Weeks (a.k.a. Pentecost) and to give their tithe to the poor every three years.
Verses 1-11 is describing something we have seen many times before, the obligation to offer first fruits to the LORD as part of the Feast of Weeks. Prior descriptions of this are either vague on the details (Ex 23:19 and Ex 34:26) or describe the communal obligation (Lev 23:17-21). That is, Lev 23 is describing the offering that is made by the priests on behalf of the community, which makes sense because Leviticus is primarily a rulebook for priests. Num 18:12-13 and Deut 18:4 describes the dispensation of the offerings, that they go to the priests.
The passage in this chapter is describing the individual obligation of every Israelite to bring their own offering to the LORD and a ritualistic proclamation that each man had to make along with his offering. We can see that there is an obligation for each individual, the community at large, and as a side effect these offerings are used to sustain the priesthood.
Verses 12-15 describe the tithe offered to the poor and the Levites. This is one of several tithes, such as the tithe to the Levites (Num 18), the tithe of your produce which is offered every year (Deut 14:22-27) and the tithe of the third year, which is what is described in this chapter (Deut 14:28-19). Out of these three tithes, the most ambiguous is the reference in Num 18 which simply says that "all the tithe" is given to the Levites. But since the two tithes in Deut 14 also specifically say that they should be shared with the Levite, I think one could argue that Num 18 is just referring to that sharing, not a separate tithe altogether. All things considered, I'm inclined to suggest that these are the only two tithes (the two tithes from Deut 14), and that Num 18 is just referring to how the people are obliged to share those tithes with the Levites. Note that there is most likely a royal tithe established later in the kingdom period, but that is not part of the covenant per se and it is only mentioned rarely (1 Sam 8:15-17).
"Tithes" are mentioned in a general sense in many places (variously throughout Lev 27, Num 18, Deut 12 and so on) but it seems to me like there are few hard references like what we have in this chapter. Given how much emphasis I have seen in the modern church on tithing as an expectation, the OT is surprisingly sparse on the topic and the NT says nothing whatsoever (to be fair, Jesus criticizes some pharisees for their diligence in tithing, but that's hardly the admonition you find in most modern churches).
Anyway, the main thrust of this passage is also a verbal pledge that the offerer must make every year, insisting that he hasn't eaten of the tithe (a crime, the tithe is to be given away), touched it while unclean (and thus sullied) or offered it to the dead, a form of ancestor worship that is strictly forbidden. He concludes by asking for the covenantal blessing.
Verse 18 calls the Israelites a "treasured possession", which is the Hebrew word "s'gullah". It is notably the same word that Moses used in Ex 19:5 when he declared the covenant to Israel the first time. This suggests a parity of sorts between these two chapters, although Ex 19 does not discuss the tithe or first fruits. However, verses 16-19 are reminiscent of Ex 19 because they both emphasize obedience to the statutes and ordinances and that the LORD would commensurately bless them. So those sections are certainly analogous.
In conclusion, I have discussed the notion of Deuteronomy as a Hittite suzerainty treaty, but for this chapter I'm not sure how it correlates. What I do know is that this chapter concludes the specific stipulations and the next chapter begins with the blessings of obedience and curses of disobedience, which is part of the standard covenantal form. I will discuss that in more depth next.