High-pressure xenon gas is an attractive detection medium for a variety of applications in fundamental and applied physics. In this paper we study the ionization and scintillation detection properties of xenon gas at 10 bar pressure. For this purpose, we use a source of alpha particles in the NEXT-DEMO time projection chamber, the large scale prototype of the NEXT-100 neutrinoless double beta decay experiment, in three different drift electric field configurations. We measure the ionization electron drift velocity and longitudinal diffusion, and compare our results to expectations based on available electron scattering cross sections on pure xenon. In addition, two types of measurements addressing the connection between the ionization and scintillation yields are performed. On the one hand we observe, for the first time in xenon gas, large event-by-event correlated fluctuations between the ionization and scintillation signals, similar to that already observed in liquid xenon. On the other hand, we study the field dependence of the average scintillation and ionization yields. Both types of measurements may shed light on the mechanism of electron-ion recombination in xenon gas for highly-ionizing particles. Finally, by comparing the response of alpha particles and electrons in NEXT-DEMO, we find no evidence for quenching of the primary scintillation light produced by alpha particles in the xenon gas.