Besides, if you were to compare Romans 8:13 to Galatians 5:19-21 and 6:8,9, you would notice that it is referring to one particular truth that is written in 3 different ways. This one truth is talking about "spiritual death" and not "physical death."
Compare Romans 8:13 that says "not inherit the kingdom of God" with Galatians 5:19-21 that says, "and reap destruction instead of reap eternal life" in Galatians 6:8,9. Truly Paul was was referencing spiritual death here (Galatians 5:21).
No, the kingdom of God is the land promised to Abraham and his Seed, who Paul says is Christ. The inheritance that Scripture refers to is that promised to Abraham and his Seed.
15 For all the land which thou seest,
to thee will I give it, and to thy seed for ever.
16 And I will make thy seed as the dust of the earth: so that if a man can number the dust of the earth, then shall thy seed also be numbered.
17 Arise, walk through the land in the length of it and in the breadth of it; for I will give it unto thee. (Gen 13:15-17 KJV)
God promised to give the land to Abraham. Abraham never received that land. The only way he can receive it is in the resurrection. God also made the same promise to Isaac and Jacob. That is why the Jews thought that they would enter the kingdom by their birthright as the seed of Abraham. However, Paul comes alone and explains that when God made the promise to Abraham and his Seed, He didn't mean all of Abraham's physical seed but rather He meant one Seed in particular and the one Seed is Christ.
6 Even as Abraham believed God, and it was accounted to him for righteousness. {accounted: or, imputed}
7 Know ye
therefore that they which are of faith, the same are the children of Abraham.
8 And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed.
9 So then
they which be of faith are blessed with faithful Abraham.
10 For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them.
11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith.
12 And the law is not of faith: but, The man that doeth them shall live in them.
13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
15 Brethren, I speak after the manner of men; Though it be but a man's covenant, yet if it be confirmed, no man disannulleth, or addeth thereto. {covenant: or, testament}
16
Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many;
but as of one, And to thy seed, which is Christ. (Gal 3:6-16 KJV)
Paul says that those who are of faith are blessed with Abraham. Paul concludes the chapter by saying that those who are Christ's are Abraham's seed and heirs according to the promise. The promise is the land. David also tells us that Christ would inherit the land.
7 I will declare the decree: the LORD hath said unto me,
Thou art my Son; this day have I begotten thee. {the decree: or, for a decree}
8 Ask of me, and
I shall give thee the heathen for thine inheritance, and the uttermost parts of the earth for thy possession. (Psa 2:7-8 KJV)
The word earth is literally translated land.
Inheriting the kingdom means to inherit the land.