Is the infinitive something a language MUST have?

So far, Txtana (my 30-day conlang) has no infinitive form of the verb.
And so far, I don't feel any need to introduce one. But in sentences
like "I like to run." (Raxo havato setu.) the sentence just didn't
feel right to me. So I modified the way those constructions are
handled, still not using an infinitive form. Instead of using two
verbs in "I like to run." Txtana now uses a passive participle form of
the first verb as if it were an adverb. So the verb "to like" (or
similar verbs like: to be able to, to be allowed to, to intend to, to
prefer to,... etc.) becomes:

raxo = like (remember 'X' is pronounced "sh")
passive = na + raxo = naraxo. (to be liked)
participle = ~e instead of ~o = naraxe. (liked-ADV/ADJ)
havato = run

Naraxe havato setu.
Is-liked run PRES-me.
I like to run. (I like running.)

liso = to permit, to allow
naliso = to be permitted, to be allowed
nalise permitted (ADJ/ADV)
Nalise havato setu.
Is-permitted run PRES-me.
I am allowed to run.
I may run.

This seems to work fine with no infinitive. Are there natlangs other
than strictly analytical ones that lack the infinitive?