The use of motion verbs to mark tense and/or aspect and/or modality is very common across the world's languages, both as part of serial verb constructions or as auxiliary verbs.
Below are some non-Indo-European language examples.
Sùpyìré, Niger-Congo family.
Serial verb construction with the verb sí 'go' indicating futurity:
(1) Zànhe sí dùfugé kɛ̀ ɛ̀ gɛ̀
rain go maize.DEF spoil
"The rain will spoil the maize."
Bambara, Niger-Congo family.
Here the motion verb na 'come' is used as an auxiliary indicating futurity:
(2) a na taa
3sg come go
"He/she will go."
Grammaticalisation of the motion verbs 'go' and 'come' as future markers is common in Bantu languages. More examples in this paper.
Squliq Atayal, Austronesian family, Taiwan.
Here we see musa' 'go' used as an auxiliary to indicate irrealis/future:
(3) musa’ m-nbu’ yaya’ =mu
IRR AF-ill mother =1S.GEN
"My mother will be ill"
George Lakoff (1993: 218) suggests that the metaphorical basis of describing time in terms of space is biologically determined: “In our visual systems, we have detectors for motion and detectors for objects/locations. We do not have detectors for time (whatever that could mean). Thus, it makes good biological sense that time should be understood in terms of things and motion.”