S. R. Faruqi:

The older poets have used tīñ  in a number of ways. The beauty of this verse is that the terms of pachisi have been used very informally ( bāzī , chaupaṛ , kachchī paṛnā , nard , ghar ), and there's also a relationship of zila between ʿishq-bāzī  (with bāzīmeaning 'game') and chaupaṛ . But the verse doesn't convey the impression that it's a game, or some frivolity or amusement. 'House' is that space from which the player begins the game, or where he arrives in order to win, and where after arriving he's no longer obliged to move from space to space ('house' to 'house').

For the moves to prove wrong or vain, and for the 'home' to be far-- that is, to be far from a protected space, or from a space such that once arrived there it wouldn't be necessary to wander from door to door-- is a good picture of the helplessness of passion. There are two interpretations of chaupaṛ ʿajab bichhāʾī . Either someone else spread out the game-board, and we are only a player; or else we ourselves have spread out the game-board, and then we ourselves are being defeated. 'Our home is far' also gestures toward the house-wrecked condition of the lover.

Even in his youth, Ghalib liked Mir's themes. The proof is this youthful [unpublished] verse of Ghalib's, which is obviously influenced by the present verse of Mir's [G{359x,6}]:

asad andeshah-e shash-dar shudan hai
nah phirye muhrah-sāñ ḳhānah bah ḳhānah

[Asad, there's the suspicion of your becoming a die/'six-door'
don't wander like a game-piece from 'house' to 'house']

The meaning of tīñcan also be tuu. In this case, addressing ʿishq-bāzī he's said, 'oh ʿishq-bāzī , you've spread a strange chaupar-board!' . But tīñ meaning tū doesn't have that suitableness, and doesn't create that 'misdirection' the way ham ne / kisī ne / tum ne ʿishq-bāzī ke tīñ ( ke liʾe ) ʿajab chaupaṛ bichhāʾī . In any case, the opinion of the late Nisar Ahmad Faruqi was that here tīñ means tū .

FWP:

SETS
MOTIFS == HOME
NAMES  
TERMS == ZILA

This one can hardly fail to recall Zauq's verse:

kam hoñge is bisāt̤ pah ham jaise bad-qimār
jo chāl ham chale so nihāyat burī chale

[on this game-board there won't be many bad players like us
whatever move we made, we moved extremely badly]

Zauq's verse feels rueful, or maybe ruefully amused at his own bad fortune and/or unskilful play; and it's energized by all the chalnā wordplay in the second line. 

But Mir's verse is melancholy-- that sigh, that āh , sets a sorrowful mood at the beginning. Then in the second line we have first the cleverness, the cuteness, of the deployment of the technical game terms of chaupar (also called chausar , also in English called 'pachisi'). Apparently a kachchii nard is a game-piece that's in a weak or vulnerable position and cannot manage to attain the 'home' goal.

Only at the very end does the flourishing of terminology mesh with the sigh in the first line-- 'our home is far'. It's impossible not to break out of the game-mode, and read 'home' as a real (or at least metaphorically real) home. Being far from home is a much sadder state than simply losing a game of pachisi; this is a culture in which to be ġharīb is to be at once alien, friendless, and wretched.

Note for grammar fans: That taʾīñ , here compressed into tīñ , is archaic. It can be the intimate second person singular, but as SRF explains, here it seems more appropriately to have its more common sense of something like 'with regard to'; in fact it's most often seen as part of a phrase, us ke taʾīñ or apne taʾīñ . Since it here appears without its normal ke, it looks a bit more opaque than it usually does.