0V is a perfectly valid value for a KVL expression. \$V_{GS1}=V_{IN} - 0V\$ is an application of KVL, and is as valid and true as \$V_{GS2} = V_B - V_X\$. Neither of those expressions is relying on transistor characteristics.
However, the statement \$V_{IN} - 0V > V_{TH1}\$ differs in two ways; firstly it is an inequality which has nothing to do with KVL, and secondly it refers to \$V_{TH2}\$ which is a transistor characteristic that KVL knows nothing about.
KVL is always true, and simply relates potentials around a loop. Inequalities describe constraints to certain values, or behaviour of certain elements under different conditions, neither of which is accounted for in KVL, or KCL.
All KVL says is "this plus that minus the other is such and such", and never makes any claims about why, or how. It doesn't account for impedance, or dynamic or conditional behaviour. It is not concerned with greater-thans or less-thans, its only claim is that potentials around a loop sum to zero.
The condition you describe for M2 to be on is incorrect or ambiguous. You stated \$V_{b,min} > V_{GS2} + V_X\$. It would be better to say that \$V_{b,min} > V_{GS(ON)2} + V_X\$, where \$V_{GS(ON)2}\$ is a constant (perhaps from a datasheet), independent of any actual measured potentials. The value \$V_{GS2}\$ is not a constant, it's the potential difference between the gate and source of M2; \$V_{GS2} = V_B - V_X\$.
If from the datasheet you find that \$V_{GS(ON)}=2.0V\$ for M2, then the statement \$V_{b,min} > 2.0V + V_X\$ is meaningful and correct, and describes the condition necessary for M2 to be on. This is very different from \$V_{b,min} > V_{GS2} + V_X\$, which is equivalent to \$V_{b,min} > (V_B - V_X) + V_X\$, making no sense at all.
If by \$V_{TH}\$ you mean \$V_{GS(ON)}\$, then the following conditions describe the MOSFETs beginbeing on. For
For M1:
$$ V_{GS1} > V_{TH1} $$ $$ V_{IN} - 0V > V_{TH1} $$
For M2:
$$ V_{GS2} > V_{TH2} $$ $$ V_B - V_X > V_{TH2} $$