The relaxation dynamics of a low molecular supercooled liquid, cresolphthalein-dimethylether (KDE), has been investigated in the vicinity of glass transition temperature by dielectric relaxation measurements. Glass transition is approached and studied by the use of isothermal and isobaric paths. Under isobaric condition, the departure of the correlation function of the alpha -relaxation from exponential decay with time (nonexponentiality) is even less than the intermediate liquids such as glycerol. However, the T-g-scaled temperature dependence of the alpha -relaxation time, tau, resembles "fragile" glass-formers like orthoterphenyl (OTP). Thus KDE, like propylene carbonate (PC) that has in common a basic chemical structural unit, is an exception to the correlation between "fragility" and nonexponentiality found to hold for most glass formers. The dielectric relaxation measurements with the application of pressure show that KDE has large pressure coefficient of the glass transition temperature, (dT(g)/dP)(P -->0), or large activation volume, typically of "fragile" glass-formers. However, unlike "fragile" glass-formers, the change of the scaled activation volume with log tau for KDE is slow, comparable with that of glycerol. The dielectric dispersion of KDE as a function of frequency at different pressure and temperature combinations has an excess high frequency wing but no resolved Johari-Goldstein beta -relaxation, resembling that of intermediate liquids. Thus the variable pressure and temperature measurements of the relaxation dynamics show that KDE (and likewise PC) behaves like a "fragile" liquid in some properties and an intermediate liquid in other properties. Previously it has been proposed that there are two distinct factors that determine the molecular dynamics of glass formers, one from thermodynamics and the other from cooperative many-body dynamics. We explain this split character of KDE and PC by the prominence of the thermodynamics factor, possibly due to the unique basic chemical structural unit they have in common. The prominent thermodynamics factor gives rise to properties, such as the T-g-scaled temperature dependence of the alpha -relaxation time and large (dT(g)/dP)(P -->0), that resemble "fragile" liquids. While the cooperative many-body dynamics in KDE and PC is weak as evidenced by low degree of nonexponentiality of the alpha -relaxation correlation function. Consequently some properties, including the shape of the dielectric dispersion, coincide with that of intermediate liquids. The explanation is supported by the comparison of adiabatic calorimetric data of PC and OTP to show that indeed the thermodynamics factor in PC is like that of a very "fragile" liquid.