"Modern Haiku" is the name of a publication, in which these poems were first published. The link you published is on their web site. I haven't submitted to them, or anyone, for a few years now. I am ambivalent about publishing.
The specific form I used for the above poems is called "haibun". It's a mixture of prose and haiku, with the links between the haiku and the prose sections obeying the same general rules as the "turn" in tanka or the links in renga, other Japanese poetic forms.