I think that Torah observance is second tier to the real idea behind the kingdom of God/heaven, which is simply that God, as the sovereign of Israel, must rule in order for justice to finally prevail. Israel/Judah languishing under the Assyrians, the Babylonians, the Medes, the Persians, the Greeks, and the Romans just will not cut it; God has to reign supreme, and not through one of those foreign powers. No, God must rule on his own merits; Israel must be a free country, possibly even the seat of its own empire; and only approved surrogates must rule over Israel in God's name (Aaronid priests and a Davidic king/messiah are the main candidates for the job).
If God rules, then of course what God says goes, and for many/most Jews that would be the Torah. But the cart cannot come before the horse. Torah observance is the effect, not the cause, of the kingdom of God being enacted on earth.
Other ideas which go along with the kingdom of God are, for example, the reconstitution of the nation of Israel in its own land and, as an accompaniment to that, the resurrection from the dead, on the grounds that it is only just for the nation's faithful forebears to participate in the kingdom of God.
Another term for the kingdom of God, essentially, is "the age to come," the age during which all wrongs will be righted and justice will prevail.
Synoptic parallels all over the place would indicate that Matthew often substitutes heaven for God in this phrase: Matthew 5.3 = Luke 6.20; Matthew 8.11 = Luke 13.28; Matthew 11.11 = Luke 7.28; Matthew 11.12 = Luke 16.16; Matthew 13.11 = Mark 4.11 = Luke 8.10; Matthew 11.24 = Mark 4.26; Matthew 13.31 = Mark 4.30 = Luke 13.18; Matthew 13.33 = Luke 13.20; Matthew 19.14 = Mark 10.14 = Luke 18.16; Matthew 19.23 = Mark 10.23 = Luke 18.24; Matthew 22.1 = Luke 14.15 (?).
A customary explanation is that periphrastic expressions were often used for God out of respect. But it is not as if Matthew avoids the term "God" or anything, not even in this expression: refer to Matthew 12.28; 19.24; 21.31, 43. So it may just be a preference.